## Liu, Jianguo

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 Author ID: liu.jian-guo Published as: Liu, Jian-Guo; Liu, Jian-guo; Liu, J.-G. Homepage: https://services.math.duke.edu/~jliu/ External Links: MGP · ORCID · Google Scholar · ResearchGate · dblp
 Documents Indexed: 271 Publications since 1984 4 Contributions as Editor Co-Authors: 115 Co-Authors with 200 Joint Publications 4,534 Co-Co-Authors
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### Co-Authors

 5 single-authored 18 Degond, Pierre 17 Gao, Yuan 13 Li, Lei 13 Pego, Robert L. 13 Wang, Cheng 11 E, Weinan 11 Jin, Shi 10 Zhou, Zhennan 8 Lu, Jianfeng 8 Wang, Jinhuan 8 Xin, Zhouping 7 Huang, Hui 7 Wang, Li 7 Wang, Wei-Cheng 6 Frouvelle, Amic 6 Xu, Xiangsheng 6 Zeng, Zhifang 5 Chen, Xiuqing 5 Gao, Yu 5 Johnston, Hans 5 Liu, Jie 4 Ai, Guo-Ping 4 Feng, Yuanyuan 4 Tian, Yu 3 Chan, Francis H. Y. 3 Chertock, Alina E. 3 Lam, F. K. 3 Marzuola, Jeremy L. 3 Pendleton, Terrance 3 Ringhofer, Christian A. 3 Tang, Min 3 Yang, Rong 3 Zhang, Yuan 2 Bian, Shen 2 Billings, Stephen A. 2 Chae, Dongho 2 Chen, Li 2 Chen, Zhong 2 Cong, Wenting 2 Coquel, Frédéric 2 Duan, Yong 2 Eslami, Mostafa 2 Goudon, Thierry 2 Guo, Qi 2 Herty, Michael Matthias 2 Huang, Yin-Liang 2 Ji, Hangjie 2 LeFloch, Philippe Gerard 2 Levermore, C. David 2 Li, Bo 2 Li, Qin 2 Lin, Ping 2 Liu, Qinghuo 2 Liu, Zhenbing 2 Liu, Zibu 2 Lu, Xiliang 2 Lu, Xinyang 2 Lu, Yulong 2 Ma, Zheng 2 Mieussens, Luc 2 Mirzazadeh, Mohammad 2 Motsch, Sébastien 2 Rezazadeh, Hadi 2 Shu, Chi-Wang 2 Tadmor, Eitan 2 Tzavaras, Athanasios E. 2 Wan, Liang 2 Witelski, Thomas P. 2 Xu, Wenqing 2 Xu, Xiaoqian 2 Yan, Bokai 2 Yang, Lianwu 2 Ye, Qing 2 You, Mengxiang 2 Yue, Yue 1 Acheritogaray, Marion 1 Aligoli, M. 1 Alshal, Hassan 1 Antman, Stuart S. 1 Baeder, James D. 1 Ban, Zhihua 1 Bao, Weizhu 1 Baral, Purna C. 1 Bosco, E. 1 Cao, Li 1 Carrillo de la Plata, José Antonio 1 Chai, Mei 1 Chainais-Hillairet, Claire 1 Chen, Chuanmiao 1 Chen, Gui-Qiang G. 1 Chen, Jian 1 Chen, Jingrun 1 Chen, Ke 1 Chen, Wenbin 1 Cheng, Zhibin 1 Chern, I-Liang 1 Childress, Stephen 1 Choi, Hwajeong 1 Curtright, Thomas L. 1 Dai, Shikun ...and 106 more Co-Authors
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### Serials

 16 Journal of Computational Physics 14 Mathematics of Computation 13 SIAM Journal on Mathematical Analysis 12 Communications in Mathematical Sciences 10 Discrete and Continuous Dynamical Systems. Series B 8 SIAM Journal on Numerical Analysis 8 Applied Mathematics Letters 6 Physica D 6 Journal of Scientific Computing 6 Methods and Applications of Analysis 5 Quarterly of Applied Mathematics 5 Journal of Nonlinear Science 4 Archive for Rational Mechanics and Analysis 4 Communications on Pure and Applied Mathematics 4 Journal of Statistical Physics 4 Nonlinearity 4 Journal of Differential Equations 4 Nonlinear Dynamics 4 International Journal of Nonlinear Sciences and Numerical Simulation 4 Communications in Computational Physics 4 Kinetic and Related Models 3 Acta Applicandae Mathematicae 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Scientific Computing 3 Multiscale Modeling & Simulation 3 Annals of Mathematical Sciences and Applications 2 Computers & Mathematics with Applications 2 Communications in Mathematical Physics 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal of Control 2 International Journal for Numerical Methods in Fluids 2 Numerische Mathematik 2 Chinese Annals of Mathematics. Series B 2 Bulletin of the Iranian Mathematical Society 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 SIAM Journal on Applied Mathematics 2 Calculus of Variations and Partial Differential Equations 2 Interfaces and Free Boundaries 2 IEEE Transactions on Image Processing 2 Acta Mathematica Scientia. Series A. (Chinese Edition) 2 Proceedings of Symposia in Applied Mathematics 2 Analysis and Mathematical Physics 2 Journal of Nanchang University. Natural Science 2 Research in the Mathematical Sciences 1 Acta Mechanica 1 Applicable Analysis 1 Computers and Fluids 1 European Journal of Physics 1 Indian Journal of Pure & Applied Mathematics 1 Inverse Problems 1 Journal of Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Mathematical Notes 1 Physica A 1 Physics Letters. B 1 Transport Theory and Statistical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Biometrika 1 IEEE Transactions on Computers 1 Transactions of the American Mathematical Society 1 Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica 1 Natural Science Journal of Xiangtan University 1 Acta Automatica Sinica 1 Parallel Computing 1 Applied Numerical Mathematics 1 Journal of Systems Science and Mathematical Sciences 1 Computational Mechanics 1 Journal of Parallel and Distributed Computing 1 European Journal of Applied Mathematics 1 Signal Processing 1 IEEE Transactions on Signal Processing 1 European Journal of Operational Research 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Physics of Fluids 1 Journal of Huazhong University of Science and Technology 1 Computational and Applied Mathematics 1 Transactions of Nanjing University of Aeronautics & Astronautics 1 Engineering Analysis with Boundary Elements 1 Discrete and Continuous Dynamical Systems 1 Matemática Contemporânea 1 Mathematical Problems in Engineering 1 Communications in Applied Analysis 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Chaos 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Applied Statistics 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 IEEE Transactions on Antennas and Propagation 1 Journal of Changsha Communications University 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 EURASIP Journal on Applied Signal Processing 1 Communications on Pure and Applied Analysis 1 Milan Journal of Mathematics 1 Journal of Huaihua University 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore ...and 14 more Serials
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### Fields

 159 Partial differential equations (35-XX) 87 Numerical analysis (65-XX) 86 Fluid mechanics (76-XX) 42 Statistical mechanics, structure of matter (82-XX) 31 Biology and other natural sciences (92-XX) 24 Probability theory and stochastic processes (60-XX) 19 Dynamical systems and ergodic theory (37-XX) 18 Mechanics of deformable solids (74-XX) 14 Computer science (68-XX) 11 Ordinary differential equations (34-XX) 8 Operator theory (47-XX) 8 Statistics (62-XX) 8 Information and communication theory, circuits (94-XX) 7 Special functions (33-XX) 6 Operations research, mathematical programming (90-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Optics, electromagnetic theory (78-XX) 5 Systems theory; control (93-XX) 4 General and overarching topics; collections (00-XX) 4 Functional analysis (46-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Real functions (26-XX) 3 Difference and functional equations (39-XX) 3 Integral transforms, operational calculus (44-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Geophysics (86-XX) 2 Potential theory (31-XX) 2 Convex and discrete geometry (52-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Differential geometry (53-XX) 1 Astronomy and astrophysics (85-XX)

### Citations contained in zbMATH Open

212 Publications have been cited 2,979 times in 1,920 Documents Cited by Year
A simple proof of the Cucker-Smale flocking dynamics and mean-field limit. Zbl 1177.92003
Ha, Seung-Yeal; Liu, Jian-Guo
2009
A coupled chemotaxis-fluid model: global existence. Zbl 1236.92013
Liu, Jian-Guo; Lorz, Alexander
2011
Kinetic formulation and global existence for the Hall-magneto-hydrodynamics system. Zbl 1251.35076
Acheritogaray, Marion; Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo
2011
Well-posedness for Hall-magnetohydrodynamics. Zbl 1297.35064
Chae, Dongho; Degond, Pierre; Liu, Jian-Guo
2014
Projection method. I: Convergence and numerical boundary layers. Zbl 0842.76052
E, Weinan; Liu, Jian-Guo
1995
Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term. Zbl 1127.76343
Johnston, Hans; Liu, Jian-Guo
2004
Thin film epitaxy with or without slope selection. Zbl 1059.35059
Li, Bo; Liu, Jian-Guo
2003
Vorticity boundary condition and related isssues for finite difference schemes. Zbl 0847.76050
E, Weinan; Liu, Jian-Guo
1996
Essentially compact schemes for unsteady viscous incompressible flows. Zbl 0853.76045
E, Weinan; Liu, Jian-Guo
1996
An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations. Zbl 1373.76284
Haack, Jeffrey; Jin, Shi; Liu, Jian-guo
2012
A high-order discontinuous Galerkin method for 2D incompressible flows. Zbl 0963.76069
Liu, Jian-Guo; Shu, Chi-Wang
2000
Gauge method for viscous incompressible flows. Zbl 1160.76329
E, Weinan; Liu, Jian-Guo
2003
Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique. Zbl 1230.74240
Jiang, C.; Han, X.; Lu, G. Y.; Liu, J.; Zhang, Z.; Bai, Y. C.
2011
Macroscopic limits and phase transition in a system of self-propelled particles. Zbl 1275.35019
Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo
2013
Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent $$m > 0$$. Zbl 1292.35061
Bian, Shen; Liu, Jian-Guo
2013
Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics. Zbl 1311.82017
Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo
2015
Stable and accurate pressure approximation for unsteady incompressible viscous flow. Zbl 1307.76029
Liu, Jian-Guo; Liu, Jie; Pego, Robert L.
2010
A note on Aubin-Lions-Dubinskiĭ lemmas. Zbl 1326.46019
Chen, Xiuqing; Jüngel, Ansgar; Liu, Jian-Guo
2014
Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. Zbl 1032.82038
Chainais-Hillairet, Claire; Liu, Jian-Guo; Peng, Yue-Jun
2003
Dynamics in a kinetic model of oriented particles with phase transition. Zbl 1248.35097
Frouvelle, Amic; Liu, Jian-Guo
2012
Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate. Zbl 1131.35058
Liu, Jian-Guo; Liu, Jie; Pego, Robert L.
2007
Epitaxial growth without slope selection: energetics, coarsening, and dynamic scaling. Zbl 1123.35327
Li, Bo; Liu, Jian-Guo
2004
Diversity of exact solutions to a (3 + 1)-dimensional nonlinear evolution equation and its reduction. Zbl 1434.35172
Yin, Yu-Hang; Ma, Wen-Xiu; Liu, Jian-Guo; Lü, Xing
2018
Convergence of vortex methods for weak solutions to the $$2-D$$ Euler equations with vortex sheet data. Zbl 0829.35098
Liu, Jian-Guo; Xin, Zhouping
1995
Hydrodynamic models of self-organized dynamics: derivation and existence theory. Zbl 1278.35153
Degond, Pierre; Liu, Jian-Guo; Motsch, Sebastien; Panferov, Vladislav
2013
Finite difference schemes for incompressible flow based on local pressure boundary conditions. Zbl 1130.76409
Johnston, Hans; Liu, Jian-Guo
2002
Accurate evaluation of electrostatics for macromolecules in solution. Zbl 1099.92500
Chern, I-Liang; Liu, Jian-Guo; Wang, Wei-Cheng
2003
Mach-number uniform asymptotic-preserving gauge schemes for compressible flows. Zbl 1210.76135
Degond, P.; Jin, S.; Liu, J.-G.
2007
Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit. Zbl 1220.65116
Liu, Jian-Guo; Mieussens, Luc
2010
The effects of numerical viscosities. I: Slowly moving shocks. Zbl 0858.76054
Jin, Shi; Liu, Jian-Guo
1996
A fourth-order scheme for incompressible Boussinesq equations. Zbl 1112.76051
Liu, Jian-Guo; Wang, Cheng; Johnston, Hans
2003
Convergence of gauge method for incompressible flow. Zbl 0968.76065
Wang, Cheng; Liu, Jian-Guo
2000
Large-scale dynamics of mean-field games driven by local Nash equilibria. Zbl 1295.91015
Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian
2014
Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition-based asymptotic-preserving method. Zbl 1375.65004
Jin, Shi; Liu, Jian-Guo; Ma, Zheng
2017
Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations. Zbl 1383.65111
Liu, Jian-Guo; Wang, Li; Zhou, Zhennan
2018
Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry. Zbl 1288.76093
Liu, Jian-Guo; Wang, Wei-Cheng
2004
Multidimensional degenerate Keller-Segel system with critical diffusion exponent $$2n/(n+2)$$. Zbl 1255.35034
Chen, Li; Liu, Jian-Guo; Wang, Jinhuan
2012
Cauchy problems for Keller-Segel type time-space fractional diffusion equation. Zbl 1427.35329
Li, Lei; Liu, Jian-Guo; Wang, Lizhen
2018
Projection method. II: Godunov-Ryabenki analysis. Zbl 0920.76056
E, Weinan; Liu, Jian-Guo
1996
Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on nonstaggered grids. Zbl 0901.76046
E, Weinan; Liu, Jian-Guo
1997
A generalized definition of Caputo derivatives and its application to fractional ODEs. Zbl 1401.26013
Li, Lei; Liu, Jian-Guo
2018
Characterization and regularity for axisymmetric solenoidal vector fields with application to Navier-Stokes equation. Zbl 1197.35195
Liu, Jian-Guo; Wang, Wei-Cheng
2009
Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria. Zbl 1298.91104
Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian
2014
Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos. Zbl 1358.65073
Huang, Hui; Liu, Jian-Guo
2016
Stable discretization of magnetohydrodynamics in bounded domains. Zbl 1278.76127
Liu, Jian-Guo; Pego, Robert
2010
Evolution of wealth in a non-conservative economy driven by local Nash equilibria. Zbl 1353.91051
Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian
2014
Convergence of a particle method and global weak solutions of a family of evolutionary PDEs. Zbl 1239.35120
Chertock, Alina; Liu, Jian-Guo; Pendleton, Terrance
2012
Macroscopic fluid models with localized kinetic upscaling effects. Zbl 1147.82331
Degond, Pierre; Liu, Jian-Guo; Mieussens, Luc
2006
Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation. Zbl 1022.76039
Wang, Cheng; Liu, Jian-Guo
2002
On generating functions of Hausdorff moment sequences. Zbl 1350.44003
Liu, Jian-Guo; Pego, Robert L.
2016
Term and variable selection for nonlinear system identification. Zbl 1050.93506
Wei, H. L.; Billings, S. A.; Liu, J.
2004
Coagulation-fragmentation model for animal group-size statistics. Zbl 1382.92260
Degond, Pierre; Liu, Jian-Guo; Pego, Robert L.
2017
Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows. Zbl 1130.76053
Liu, Jian-Guo; Wang, Wei-Cheng
2006
Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions. Zbl 0915.35069
LeFloch, Philippe G.; Liu, Jian-Guo
1999
Convergence of the point vortex method for 2-D vortex sheet. Zbl 0977.76069
Liu, Jian-Guo; Xin, Zhouping
2001
Finite difference schemes for incompressible flows in the velocity-impulse density formulation. Zbl 0870.76048
E, Weinan; Liu, Jian-Guo
1997
Mean-field games and model predictive control. Zbl 1383.93029
Degond, Pierre; Herty, Michael; Liu, Jian-Guo
2017
Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow. Zbl 1054.76025
Ghil, Michael; Liu, Jian-Guo; Wang, Cheng; Wang, Shouhong
2004
Analysis of a fourth-order finite difference method for the incompressible Boussinesq equations. Zbl 1055.76042
Wang, Cheng; Liu, Jian-Guo; Johnston, Hans
2004
Nonlinear stability of discrete shocks for systems of conservation laws. Zbl 0807.35087
Liu, Jian-Guo; Xin, Zhouping
1993
Projection method. III: Spatial discretization on the staggered grid. Zbl 1058.76043
E, Weinan; Liu, Jian-Guo
2002
Spectral indicator method for a non-selfadjoint Steklov eigenvalue problem. Zbl 1422.65361
Liu, J.; Sun, J.; Turner, T.
2019
Random batch methods (RBM) for interacting particle systems. Zbl 1453.82065
Jin, Shi; Li, Lei; Liu, Jian-Guo
2020
Some compactness criteria for weak solutions of time fractional PDEs. Zbl 1403.35318
Li, Lei; Liu, Jian-Guo
2018
The reconstruction of upwind fluxes for conservation laws: Its behavior in dynamic and steady state calculations. Zbl 0935.76048
Choi, Hwajeong; Liu, Jian-Guo
1998
Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation. Zbl 0858.76073
Liu, Jian-Guo; Xin, Zhouping
1996
A degenerate $$p$$-Laplacian Keller-Segel model. Zbl 1364.35162
Cong, Wenting; Liu, Jian-Guo
2016
An energy-preserving MAC-Yee scheme for the incompressible MHD equation. Zbl 0999.76096
Liu, Jian-Guo; Wang, Wei-Cheng
2001
Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit. Zbl 1173.82032
Degond, Pierre; Liu, Jian-Guo; Vignal, Marie-Hélène
2008
Propagation of chaos for large Brownian particle system with Coulomb interaction. Zbl 1355.82025
Liu, Jian-Guo; Yang, Rong
2016
A random particle blob method for the Keller-Segel equation and convergence analysis. Zbl 1355.60092
Liu, Jian-Guo; Yang, Rong
2017
Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation. Zbl 1387.35024
Degond, Pierre; Liu, Jian-Guo
2012
A note on $$L^\infty$$-bound and uniqueness to a degenerate Keller-Segel model. Zbl 1335.35103
Liu, Jian-Guo; Wang, Jinhuan
2016
Simple finite element method in vorticity formulation for incompressible flows. Zbl 0977.76048
Liu, Jian-Guo; E, Weinan
2001
Multiple-soliton solutions, soliton-type solutions and rational solutions for the $$(3+1)$$-dimensional generalized shallow water equation in oceans, estuaries and impoundments. Zbl 1349.35058
Zeng, Zhi-Fang; Liu, Jian-Guo; Nie, Bin
2016
Blow-up, zero $$\alpha$$ limit and the Liouville type theorem for the Euler-poincaré equations. Zbl 1251.35075
Chae, Dongho; Liu, Jian-Guo
2012
Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime. Zbl 1377.35145
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng
2017
Error estimate of a random particle blob method for the Keller-Segel equation. Zbl 1368.65207
Huang, Hui; Liu, Jian-Guo
2017
A new nonlinear interval programming method for uncertain problems with dependent interval variables. Zbl 1338.90487
Jiang, C.; Zhang, Z. G.; Zhang, Q. F.; Han, X.; Xie, H. C.; Liu, J.
2014
An accurate front capturing scheme for tumor growth models with a free boundary limit. Zbl 1395.65050
Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan
2018
Existence theorems for a multidimensional crystal surface model. Zbl 1355.35091
Liu, Jian-Guo; Xu, Xiangsheng
2016
Partial regularity of weak solutions to a PDE system with cubic nonlinearity. Zbl 1383.35042
Liu, Jian-Guo; Xu, Xiangsheng
2018
Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces. Zbl 1365.35174
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng
2017
Elastic collisions among peakon solutions for the Camassa-Holm equation. Zbl 1326.35309
Chertock, Alina; Liu, Jian-Guo; Pendleton, Terrance
2015
Concepts and application of time-limiters to high resolution schemes. Zbl 1081.76582
Duraisamy, Karthikeyan; Baeder, James D.; Liu, Jian-Guo
2003
Large oscillations arising in a dispersive numerical scheme. Zbl 0887.65098
Levermore, C. D.; Liu, Jian-Guo
1996
$$L^ 1$$-stability of stationary discrete shocks. Zbl 0795.65059
Liu, Jian-Guo; Xin, Zhouping
1993
Lump-type solutions and interaction solutions for the $$(2+1)$$-dimensional generalized fifth-order KdV equation. Zbl 1410.35175
Liu, Jian-Guo
2018
Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows. Zbl 1349.82046
Goudon, Thierry; Jin, Shi; Liu, Jian-Guo; Yan, Bokai
2013
Analysis of a sequential regularization method for the unsteady Navier-Stokes equations. Zbl 1285.76018
Lu, Xiliang; Lin, Ping; Liu, Jian-Guo
2008
Learning interacting particle systems: diffusion parameter estimation for aggregation equations. Zbl 1412.65171
Huang, Hui; Liu, Jian-Guo; Lu, Jianfeng
2019
Multiple soliton solutions, soliton-type solutions and rational solutions for the (3+1)-dimensional potential-YTSF equation. Zbl 1339.35264
Liu, Jianguo; Zeng, Zhifang
2014
Gauge finite element method for incompressible flows. Zbl 1032.76038
E, Weinan; Liu, Jian-Guo
2000
Continuous and discrete one dimensional autonomous fractional ODEs. Zbl 1405.34008
Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo; Xu, Xiaoqian
2018
On the diffusion approximation of nonconvex stochastic gradient descent. Zbl 1421.90121
Hu, Wenqing; Li, Chris Junchi; Li, Lei; Liu, Jian-Guo
2019
Ultra-contractivity for Keller-Segel model with diffusion exponent $$m>1-2/d$$. Zbl 1295.35271
Bian, Shen; Liu, Jian-Guo; Zou, Chen
2014
Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 1439.35418
2019
Refined hyper-contractivity and uniqueness for the Keller-Segel equations. Zbl 1330.35040
Liu, Jian-Guo; Wang, Jinhuan
2016
A fourth order numerical method for the primitive equations formulated in mean vorticity. Zbl 1364.76136
Liu, Jian-Guo; Wang, Cheng
2008
Long-time dynamics for a simple aggregation equation on the sphere. Zbl 1442.82031
Frouvelle, Amic; Liu, Jian-Guo
2019
Convergence of the random batch method for interacting particles with disparate species and weights. Zbl 1466.65011
Jin, Shi; Li, Lei; Liu, Jian-Guo
2021
Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface. Zbl 07376314
Gao, Yuan; Liu, Jian-Guo
2021
Large time behavior, bi-Hamiltonian structure, and kinetic formulation for a complex Burgers equation. Zbl 1456.35033
Gao, Yu; Gao, Yuan; Liu, Jian-Guo
2021
Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space. Zbl 1471.35268
Gao, Yuan; Liu, Jian-Guo; Luo, Tao; Xiang, Yang
2021
Breather wave and lump-type solutions of new $$(3 + 1)$$-dimensional Boiti-Leon-Manna-Pempinelli equation in incompressible fluid. Zbl 1470.35121
Liu, Jian-Guo; Wazwaz, Abdul-Majid
2021
Existence and rigidity of the vectorial Peierls-Nabarro model for dislocations in high dimensions. Zbl 1478.35199
Gao, Yuan; Liu, Jian-Guo; Liu, Zibu
2021
Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: derivations and computations. Zbl 1483.76063
Gao, Yuan; Liu, Jian-Guo
2021
Random batch methods (RBM) for interacting particle systems. Zbl 1453.82065
Jin, Shi; Li, Lei; Liu, Jian-Guo
2020
A stochastic version of Stein variational gradient descent for efficient sampling. Zbl 1444.62043
Li, Lei; Li, Yingzhou; Liu, Jian-Guo; Liu, Zibu; Lu, Jianfeng
2020
Large time behaviors of upwind schemes and $$B$$-schemes for Fokker-Planck equations on $$\mathbb{R}$$ by jump processes. Zbl 1442.65214
Li, Lei; Liu, Jian-Guo
2020
Global existence for Nernst-Planck-Navier-Stokes system in $$\mathbb{R}^n$$. Zbl 1464.35186
Liu, Jian-Guo; Wang, Jinhuan
2020
Exact periodic cross-kink wave solutions for the $$(2+1)$$-dimensional Korteweg-de Vries equation. Zbl 1452.35062
Liu, Jian-Guo; Ye, Qing
2020
An adaptive nested complex source beam method for electromagnetic scattering of composite conducting-dielectric objects. Zbl 1464.78010
Wang, K. C.; Liu, J.; Xu, J. H.; Fan, X. T.; Zhang, L. R.
2020
Long time behavior of dynamic solution to Peierls-Nabarro dislocation model. Zbl 1448.35044
Gao, Yuan; Liu, Jian-Guo
2020
The dynamical behavior of mixed type lump solutions on the $$(3 + 1)$$-dimensional generalized Kadomtsev-Petviashvili-Boussinesq equation. Zbl 07446859
2020
Uniform-in-time weak error analysis for stochastic gradient descent algorithms via diffusion approximation. Zbl 1440.60073
Feng, Yuanyuan; Gao, Tingran; Li, Lei; Liu, Jian-Guo; Lu, Yulong
2020
Existence results of multiple solutions for a $$2n$$th-order finite difference equation. Zbl 1444.47076
You, Mengxiang; Tian, Yu; Yue, Yue; Liu, Jianguo
2020
Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects. Zbl 1443.35085
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng; Marzuola, Jeremy L.
2020
On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system. Zbl 1466.35344
Huang, Hui; Liu, Jian-Guo; Pickl, Peter
2020
A class of functional inequalities and their applications to fourth-order nonlinear parabolic equations. Zbl 1462.35104
Liu, Jian-Guo; Xu, Xiangsheng
2020
Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation. Zbl 1469.37049
Hosseini, K.; Mirzazadeh, M.; Aligoli, M.; Eslami, M.; Liu, J. G.
2020
Spectral indicator method for a non-selfadjoint Steklov eigenvalue problem. Zbl 1422.65361
Liu, J.; Sun, J.; Turner, T.
2019
Learning interacting particle systems: diffusion parameter estimation for aggregation equations. Zbl 1412.65171
Huang, Hui; Liu, Jian-Guo; Lu, Jianfeng
2019
On the diffusion approximation of nonconvex stochastic gradient descent. Zbl 1421.90121
Hu, Wenqing; Li, Chris Junchi; Li, Lei; Liu, Jian-Guo
2019
Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 1439.35418
2019
Long-time dynamics for a simple aggregation equation on the sphere. Zbl 1442.82031
Frouvelle, Amic; Liu, Jian-Guo
2019
On the mean field limit for Brownian particles with Coulomb interaction in 3D. Zbl 1431.82019
Li, Lei; Liu, Jian-Guo; Yu, Pu
2019
Propagation of chaos for the Keller-Segel equation with a logarithmic cut-off. Zbl 1442.35199
Liu, Jian-Guo; Yang, Rong
2019
Least action principles for incompressible flows and geodesics between shapes. Zbl 1428.35376
Liu, Jian-Guo; Pego, Robert L.; Slepčev, Dejan
2019
Collisions between lump and soliton solutions. Zbl 1412.35054
Liu, Jian-Guo
2019
Global stability for solutions to the exponential PDE describing epitaxial growth. Zbl 1418.35215
Liu, Jian-Guo; Strain, Robert M.
2019
Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics. Zbl 1418.35225
Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan
2019
Stripe solitons and lump solutions for a generalized Kadomtsev-Petviashvili equation with variable coefficients in fluid mechanics. Zbl 1437.35583
Liu, Jian-Guo; Ye, Qing
2019
The solitary wave, rogue wave and periodic solutions for the $$(3+1)$$-dimensional soliton equation. Zbl 1406.35088
Liu, Jian-Guo; You, Meng-Xiang; Zhou, Li; Ai, Guo-Ping
2019
Gradient flow approach to an exponential thin film equation: global existence and latent singularity. Zbl 1442.35185
Gao, Yuan; Liu, Jian-Guo; Lu, Xin Yang
2019
A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows. Zbl 07105241
Li, Lei; Liu, Jian-Guo
2019
Closed-form solutions of unsteady two-fluid flow in a tube. Zbl 1418.76060
Liu, J.; Wang, C. Y.
2019
The conducting ring viewed as a wormhole. Zbl 1421.78009
Curtright, T.; Alshal, H.; Baral, P.; Huang, S.; Liu, J.; Tamang, K.; Zhang, X.; Zhang, Y.
2019
On the rate of convergence of empirical measure in $$\infty$$-Wasserstein distance for unbounded density function. Zbl 1447.60008
Liu, Anning; Liu, Jian-Guo; Lu, Yulong
2019
Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model. Zbl 1451.35074
Liu, Jian-Guo; Lu, Jianfeng; Margetis, Dionisios; Marzuola, Jeremy L.
2019
Multi-scale modelling of granular materials: numerical framework and study on micro-structural features. Zbl 1464.74041
Liu, J.; Bosco, E.; Suiker, A. S. J.
2019
Well-posedness and derivative blow-up for a dispersionless regularized shallow water system. Zbl 1428.35375
Liu, Jian-Guo; Pego, Robert L.; Pu, Yue
2019
Diversity of exact solutions to a (3 + 1)-dimensional nonlinear evolution equation and its reduction. Zbl 1434.35172
Yin, Yu-Hang; Ma, Wen-Xiu; Liu, Jian-Guo; Lü, Xing
2018
Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations. Zbl 1383.65111
Liu, Jian-Guo; Wang, Li; Zhou, Zhennan
2018
Cauchy problems for Keller-Segel type time-space fractional diffusion equation. Zbl 1427.35329
Li, Lei; Liu, Jian-Guo; Wang, Lizhen
2018
A generalized definition of Caputo derivatives and its application to fractional ODEs. Zbl 1401.26013
Li, Lei; Liu, Jian-Guo
2018
Some compactness criteria for weak solutions of time fractional PDEs. Zbl 1403.35318
Li, Lei; Liu, Jian-Guo
2018
An accurate front capturing scheme for tumor growth models with a free boundary limit. Zbl 1395.65050
Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan
2018
Partial regularity of weak solutions to a PDE system with cubic nonlinearity. Zbl 1383.35042
Liu, Jian-Guo; Xu, Xiangsheng
2018
Lump-type solutions and interaction solutions for the $$(2+1)$$-dimensional generalized fifth-order KdV equation. Zbl 1410.35175
Liu, Jian-Guo
2018
Continuous and discrete one dimensional autonomous fractional ODEs. Zbl 1405.34008
Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo; Xu, Xiaoqian
2018
Semigroups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations. Zbl 1417.60065
Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo
2018
Online learning in optical tomography: a stochastic approach. Zbl 06899031
Chen, Ke; Li, Qin; Liu, Jian-Guo
2018
A note on deconvolution with completely monotone sequences and discrete fractional calculus. Zbl 1476.47029
Li, Lei; Liu, Jian-Guo
2018
Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface. Zbl 1401.35204
Gao, Yuan; Liu, Jian-Guo; Lu, Xin Yang; Xu, Xiangsheng
2018
Interaction behaviors for the $$(2+1)$$-dimensional Sawada-Kotera equation. Zbl 1398.37064
Liu, Jian-Guo
2018
A note on one-dimensional time fractional odes. Zbl 06892563
Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo; Xu, Xiaoqian
2018
New double-periodic soliton solutions for the $$(2+1)$$-dimensional breaking soliton equation. Zbl 1402.35234
Liu, Jian-Guo; Tian, Yu
2018
The modified Camassa-Holm equation in Lagrangian coordinates. Zbl 1404.35105
Gao, Yu; Liu, Jian-Guo
2018
A vicinal surface model for epitaxial growth with logarithmic free energy. Zbl 1403.35123
Gao, Yuan; Ji, Hangjie; Liu, Jian-Guo; Witelski, Thomas P.
2018
Double-periodic soliton solutions for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation in incompressible fluid. Zbl 1420.35247
Liu, Jian-Guo
2018
New non-traveling wave solutions for the $$(3+1)$$-dimensional Boiti-Leon-Manna-Pempinelli equation. Zbl 1459.35071
Liu, Jian-Guo; Tian, Yu; Hu, Jian-Guo
2018
Existence of infinitely many solutions for fourth-order impulsive differential equations. Zbl 1393.34039
Yue, Yue; Tian, Yu; Zhang, Min; Liu, Jianguo
2018
A dispersive regularization for the modified Camassa-Holm equation. Zbl 1403.35075
Gao, Yu; Li, Lei; Liu, Jian-Guo
2018
Analogues of some determinantal inequalities for sector matrices. Zbl 1407.15022
Liu, J.; Sheng, X.
2018
New multiple periodic-soliton solutions for the (3+1)-dimensional potential-YTSF equation. Zbl 1438.35094
Wei, Huan; Yang, Lianwu; Liu, Jianguo
2018
$$p$$-Euler equations and $$p$$-Navier-Stokes equations. Zbl 1384.35093
Li, Lei; Liu, Jian-Guo
2018
Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws. Zbl 1384.65052
Coquel, Frédéric; Jin, Shi; Liu, Jian-Guo; Wang, Li
2018
Locally $$E$$-solid epigroups. Zbl 1452.20056
Liu, J. G.
2018
Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition-based asymptotic-preserving method. Zbl 1375.65004
Jin, Shi; Liu, Jian-Guo; Ma, Zheng
2017
Coagulation-fragmentation model for animal group-size statistics. Zbl 1382.92260
Degond, Pierre; Liu, Jian-Guo; Pego, Robert L.
2017
Mean-field games and model predictive control. Zbl 1383.93029
Degond, Pierre; Herty, Michael; Liu, Jian-Guo
2017
A random particle blob method for the Keller-Segel equation and convergence analysis. Zbl 1355.60092
Liu, Jian-Guo; Yang, Rong
2017
Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime. Zbl 1377.35145
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng
2017
Error estimate of a random particle blob method for the Keller-Segel equation. Zbl 1368.65207
Huang, Hui; Liu, Jian-Guo
2017
Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces. Zbl 1365.35174
Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng
2017
Explicit and implicit TVD schemes for conservation laws with Caputo derivatives. Zbl 1371.65083
Liu, Jian-Guo; Ma, Zheng; Zhou, Zhennan
2017
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem. Zbl 1386.82053
Li, Lei; Liu, Jian-Guo; Lu, Jianfeng
2017
Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions. Zbl 1371.35142
Liu, Jian-Guo; Xu, Xiangsheng
2017
Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis. Zbl 1390.35136
Huang, Hui; Liu, Jian-Guo
2017
Continuum dynamics of the intention field under weakly cohesive social interaction. Zbl 1362.82033
Degond, Pierre; Liu, Jian-Guo; Merino-Aceituno, Sara; Tardiveau, Thomas
2017
Global convergence of a sticky particle method for the modified Camassa-Holm equation. Zbl 1458.35117
Gao, Yu; Liu, Jian-Guo
2017
Uniform $$L^{\infty}$$ boundedness for a degenerate parabolic-parabolic Keller-Segel model. Zbl 1360.35106
Cong, Wenting; Liu, Jian-Guo
2017
A class of exact solutions of $$(3+1)$$-dimensional generalized B-type Kadomtsev-Petviashvili equation. Zbl 1401.35272
Liu, Shuang; Ding, Yao; Liu, Jian-Guo
2017
Global existence for a thin film equation with subcritical mass. Zbl 1360.35183
Liu, Jian-Guo; Wang, Jinhuan
2017
A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation. Zbl 1357.35176
Liu, Jian-Guo; Wang, Jinhuan
2017
Global existence of solutions to a tear film model with locally elevated evaporation rates. Zbl 1376.76008
Gao, Yuan; Ji, Hangjie; Liu, Jian-Guo; Witelski, Thomas P.
2017
Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos. Zbl 1358.65073
Huang, Hui; Liu, Jian-Guo
2016
On generating functions of Hausdorff moment sequences. Zbl 1350.44003
Liu, Jian-Guo; Pego, Robert L.
2016
A degenerate $$p$$-Laplacian Keller-Segel model. Zbl 1364.35162
Cong, Wenting; Liu, Jian-Guo
2016
Propagation of chaos for large Brownian particle system with Coulomb interaction. Zbl 1355.82025
Liu, Jian-Guo; Yang, Rong
2016
A note on $$L^\infty$$-bound and uniqueness to a degenerate Keller-Segel model. Zbl 1335.35103
Liu, Jian-Guo; Wang, Jinhuan
2016
Multiple-soliton solutions, soliton-type solutions and rational solutions for the $$(3+1)$$-dimensional generalized shallow water equation in oceans, estuaries and impoundments. Zbl 1349.35058
Zeng, Zhi-Fang; Liu, Jian-Guo; Nie, Bin
2016
Existence theorems for a multidimensional crystal surface model. Zbl 1355.35091
Liu, Jian-Guo; Xu, Xiangsheng
2016
Refined hyper-contractivity and uniqueness for the Keller-Segel equations. Zbl 1330.35040
Liu, Jian-Guo; Wang, Jinhuan
2016
On a Schrödinger-Landau-Lifshitz system: variational structure and numerical methods. Zbl 1352.65388
Chen, Jingrun; Liu, Jian-Guo; Zhou, Zhennan
2016
A stochastic scaled boundary finite element method. Zbl 1439.74445
Long, X. Y.; Jiang, C.; Yang, C.; Han, X.; Gao, W.; Liu, J.
2016
Exact periodic cross-kink wave solutions for the new $$(2+1)$$-dimensional KdV equation in fluid flows and plasma physics. Zbl 1378.35270
Liu, Jian-Guo; Du, Jian-Qiang; Zeng, Zhi-Fang; Ai, Guo-Ping
2016
Error estimate of the particle method for the $$b$$-equation. Zbl 1346.35032
Duan, Yong; Liu, Jian-Guo
2016
Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics. Zbl 1311.82017
Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo
2015
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### Cited by 2,358 Authors

 87 Liu, Jianguo 77 Ha, Seung-Yeal 48 Degond, Pierre 36 Carrillo de la Plata, José Antonio 31 Jin, Shi 27 Wang, Cheng 24 Shen, Jie 23 Choi, Young-Pil 21 Zhou, Yong 20 Kim, Jeongho 20 Winkler, Michael 18 Xiang, Zhaoyin 18 Yang, Xiaofeng 18 Zhang, Xiongtao 17 Rebholz, Leo G. 16 Fan, Jishan 15 Chen, Wenbin 14 Pareschi, Lorenzo 13 Tadmor, Eitan 12 Chae, Dongho 12 Dimarco, Giacomo 12 He, Yinnian 12 Qiao, Zhonghua 12 Qiu, Jingmei 11 Gao, Yuan 11 Jüngel, Ansgar 11 Park, Jinyeong 11 Zhang, Qian 11 Zheng, Jiashan 10 Albi, Giacomo 10 Bellomo, Nicola 10 Feng, Xinlong 10 Kang, Moon-Jin 10 Kim, Doheon 10 Kim, Dohyun 10 Li, Zhuchun 10 Liu, Chun 10 Liu, Liu 10 Liu, Yicheng 10 Schütz, Jochen 10 Shim, Woojoo 10 Wang, Xiao 10 Xin, Zhouping 9 Ko, Dongnam 9 Liu, Zuhan 9 Pego, Robert L. 9 Peszek, Jan 9 Wang, Li 9 Wang, Yulan 9 Wise, Steven M. 9 Yamazaki, Kazuo 9 Zhao, Xiaopeng 9 Zhou, Zhennan 8 Bae, Hyeong-Ohk 8 Guermond, Jean-Luc 8 Hou, Thomas Yizhao 8 Huang, Hui 8 Li, Lei 8 Li, Zhilin 8 Motsch, Sébastien 8 Shu, Ruiwen 8 Tan, Changhui 8 Wang, Jinhuan 8 Xu, Xiangsheng 8 Zhang, Guodong 7 Cancès, Clément 7 Chainais-Hillairet, Claire 7 Dong, Jiu-Gang 7 Frouvelle, Amic 7 Goudon, Thierry 7 Jiu, Quansen 7 Ju, Lili 7 Jung, Jinwook 7 Lai, Mingchih 7 Layton, William J. 7 Liu, Hailiang 7 Merino-Aceituno, Sara 7 Shvydkoy, Roman V. 7 Si, Zhiyong 7 Soler, Juan S. 7 Vignal, Marie-Hélène 7 Zanella, Mattia 7 Zhou, Ling 7 Zhu, Mingxuan 6 Bassi, Francesco 6 Ben-Artzi, Matania 6 Bian, Shen 6 Chertock, Alina E. 6 Crivellini, Andrea 6 Daus, Esther S. 6 Deluzet, Fabrice 6 Filbet, Francis 6 Fishelov, Dalia 6 Gala, Sadek 6 Gao, Yu 6 Haskovec, Jan 6 Hayat, Tasawar 6 Herty, Michael Matthias 6 Kaiser, Klaus Hermann 6 Kang, Kyungkeun ...and 2,258 more Authors
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### Cited in 248 Serials

 222 Journal of Computational Physics 99 Journal of Differential Equations 78 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 76 Journal of Scientific Computing 43 Mathematics of Computation 41 Computers and Fluids 41 Discrete and Continuous Dynamical Systems. Series B 39 Computers & Mathematics with Applications 38 Journal of Mathematical Analysis and Applications 37 SIAM Journal on Mathematical Analysis 36 Computer Methods in Applied Mechanics and Engineering 34 Nonlinear Analysis. Real World Applications 33 ZAMP. Zeitschrift für angewandte Mathematik und Physik 32 Archive for Rational Mechanics and Analysis 32 Journal of Computational and Applied Mathematics 29 Applied Mathematics and Computation 29 Physica D 27 Journal of Mathematical Physics 27 Journal of Statistical Physics 27 SIAM Journal on Numerical Analysis 27 SIAM Journal on Scientific Computing 27 Discrete and Continuous Dynamical Systems 26 Applied Mathematics Letters 24 Numerische Mathematik 24 Kinetic and Related Models 23 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 22 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 22 Communications in Computational Physics 21 Applied Numerical Mathematics 19 Journal of Nonlinear Science 19 Multiscale Modeling & Simulation 17 Nonlinearity 15 International Journal for Numerical Methods in Fluids 15 Acta Applicandae Mathematicae 15 Communications on Pure and Applied Analysis 14 Communications in Mathematical Physics 14 Journal of Fluid Mechanics 14 Calculus of Variations and Partial Differential Equations 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 Numerical Methods for Partial Differential Equations 13 Journal of Mathematical Fluid Mechanics 12 Quarterly of Applied Mathematics 11 Journal of Evolution Equations 11 Networks and Heterogeneous Media 10 Applicable Analysis 10 SIAM Journal on Applied Mathematics 9 Communications in Partial Differential Equations 9 Communications in Nonlinear Science and Numerical Simulation 8 Journal of Functional Analysis 8 Applied Mathematical Modelling 7 Communications on Pure and Applied Mathematics 7 Proceedings of the American Mathematical Society 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 Physics of Fluids 7 Boundary Value Problems 6 SIAM Journal on Control and Optimization 6 Mathematical Biosciences and Engineering 5 Journal of Mathematical Biology 5 Mathematical Methods in the Applied Sciences 5 Applied Mathematics and Optimization 5 Monatshefte für Mathematik 5 Advances in Computational Mathematics 4 Inverse Problems 4 Physica A 4 Advances in Mathematics 4 Mathematics and Computers in Simulation 4 International Journal of Computer Mathematics 4 SIAM Review 4 Computational and Applied Mathematics 4 NoDEA. Nonlinear Differential Equations and Applications 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Chaos 4 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Computational Methods in Applied Mathematics 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 International Journal of Numerical Analysis and Modeling 4 Science China. Mathematics 4 Journal of Applied Analysis and Computation 4 AIMS Mathematics 3 Journal of the Franklin Institute 3 Bulletin of Mathematical Biology 3 BIT 3 Zeitschrift für Analysis und ihre Anwendungen 3 Chinese Annals of Mathematics. Series B 3 Japan Journal of Industrial and Applied Mathematics 3 Mathematical Problems in Engineering 3 Nonlinear Dynamics 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Acta Mathematica Sinica. English Series 3 Journal of Machine Learning Research (JMLR) 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Journal of Numerical Mathematics 3 SIAM Journal on Applied Dynamical Systems 3 Analysis and Applications (Singapore) 3 Journal of Hyperbolic Differential Equations 3 Advances in Difference Equations 3 Discrete and Continuous Dynamical Systems. Series S 3 Molecular Based Mathematical Biology 3 Journal of Function Spaces ...and 148 more Serials
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### Cited in 44 Fields

 1,164 Partial differential equations (35-XX) 891 Fluid mechanics (76-XX) 700 Numerical analysis (65-XX) 447 Biology and other natural sciences (92-XX) 230 Statistical mechanics, structure of matter (82-XX) 91 Ordinary differential equations (34-XX) 82 Probability theory and stochastic processes (60-XX) 64 Mechanics of deformable solids (74-XX) 59 Dynamical systems and ergodic theory (37-XX) 55 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 47 Calculus of variations and optimal control; optimization (49-XX) 47 Systems theory; control (93-XX) 40 Mechanics of particles and systems (70-XX) 33 Optics, electromagnetic theory (78-XX) 28 Operator theory (47-XX) 24 Computer science (68-XX) 22 Classical thermodynamics, heat transfer (80-XX) 21 Quantum theory (81-XX) 20 Real functions (26-XX) 19 Integral equations (45-XX) 19 Operations research, mathematical programming (90-XX) 15 Geophysics (86-XX) 12 Functional analysis (46-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 10 Combinatorics (05-XX) 10 Statistics (62-XX) 9 Special functions (33-XX) 9 Global analysis, analysis on manifolds (58-XX) 8 Functions of a complex variable (30-XX) 8 Astronomy and astrophysics (85-XX) 7 Integral transforms, operational calculus (44-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 General and overarching topics; collections (00-XX) 5 Measure and integration (28-XX) 5 Difference and functional equations (39-XX) 5 Approximations and expansions (41-XX) 5 Differential geometry (53-XX) 3 Number theory (11-XX) 3 Information and communication theory, circuits (94-XX) 2 Potential theory (31-XX) 2 Sequences, series, summability (40-XX) 1 Nonassociative rings and algebras (17-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX)