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## Garcke, Harald

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 Author ID: garcke.harald Published as: Garcke, H.; Garcke, Harald External Links: MGP · Wikidata · GND
 Documents Indexed: 145 Publications since 1993, including 5 Books
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#### Co-Authors

 9 single-authored 40 Barrett, John W. 39 Nürnberg, Robert 15 Lam, Kei Fong 10 Styles, Vanessa 9 Abels, Helmut 8 Blank, Luise 7 Nestler, Britta 6 Hecht, Claudia 6 Hinze, Michael 6 Kohsaka, Yoshihito 6 Stinner, Bjorn 5 Eck, Christof 5 Elliott, Charles M. 5 Ito, Kazuo 5 Kahle, Christian 4 Benninghoff, Heike 4 Depner, Daniel 4 Grün, Günther 4 Knabner, Peter 4 Sarbu, Lavinia 4 Stoth, Barbara E. E. 4 Weikard, Ulrich 3 Blowey, James F. 3 Dal Passo, Roberta 2 Butz, Martin V. 2 Ebenbeck, Matthias 2 Farshbaf-Shaker, Mohammad Hassan 2 Menzel, Julia H. 2 Müller, Lars 2 Niethammer, Barbara 2 Pluda, Alessandra 2 Röger, Matthias 2 Rumpf, Martin 2 Rupprecht, Christoph 2 Signori, Andrea 2 Sitka, Emanuel 2 Weber, Josef 1 Agosti, Abramo 1 Alfaro, Matthieu 1 Arab, Nasrin 1 Bertsch, Michiel 1 Bronsard, Lia 1 Ciarletta, Pasquale 1 Dede, Luca 1 Escher, Joachim 1 Gößwein, M. 1 Hassan Farshbaf-Shaker, M. 1 Hilhorst, Danielle 1 Kampmann, Johannes 1 Knopf, Patrik 1 Kornhuber, Ralf 1 Kraus, Christiane 1 Kwak, David Jung Chul 1 Lenz, Martin 1 Maier-Paape, Stanislaus 1 Matano, Hiroshi 1 Matioc, Bogdan-Vasile 1 Metzger, Stefan 1 Novick-Cohen, Amy 1 Peletier, Mark Adriaan 1 Rätz, Andreas 1 Rocca, Elisabetta 1 Schatzle, Reiner 1 Schaubeck, Stefan 1 Ševčovič, Daniel 1 Srisupattarawanit, Tarin 1 Sturzenhecker, Thomas 1 Voigt, Axel 1 Wendler, Frank 1 Wieland, Sandra 1 Yayla, Sema
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#### Serials

 7 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 7 SIAM Journal on Mathematical Analysis 7 Interfaces and Free Boundaries 6 IMA Journal of Numerical Analysis 6 Numerische Mathematik 5 Journal of Computational Physics 5 Advances in Mathematical Sciences and Applications 4 SIAM Journal on Numerical Analysis 4 Advances in Differential Equations 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Journal of Differential Equations 3 Physica D 3 European Journal of Applied Mathematics 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 SIAM Journal on Scientific Computing 3 Springer-Lehrbuch 2 Mathematics of Computation 2 Applied Mathematics and Optimization 2 Hokkaido Mathematical Journal 2 Mathematische Nachrichten 2 SIAM Journal on Control and Optimization 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Numerical Methods for Partial Differential Equations 2 Journal of Scientific Computing 2 SIAM Journal on Applied Mathematics 2 Journal of Mathematical Fluid Mechanics 2 Journal of Evolution Equations 2 Communications in Mathematical Sciences 2 Oberwolfach Reports 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 SIAM Journal on Imaging Sciences 2 Discrete and Continuous Dynamical Systems. Series S 1 Archive for Rational Mechanics and Analysis 1 Computer Methods in Applied Mechanics and Engineering 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematical Methods in the Applied Sciences 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Applied Numerical Mathematics 1 Communications in Partial Differential Equations 1 Journal of Mathematical Imaging and Vision 1 Advances in Computational Mathematics 1 Discrete and Continuous Dynamical Systems 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 IEEE Transactions on Image Processing 1 Nonlinear Analysis. Real World Applications 1 Communications on Pure and Applied Analysis 1 Bonner Mathematische Schriften 1 Communications in Computational Physics 1 Geometric Flows 1 AIMS Mathematics 1 Springer Undergraduate Mathematics Series 1 SMAI Journal of Computational Mathematics
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#### Fields

 111 Partial differential equations (35-XX) 56 Numerical analysis (65-XX) 42 Fluid mechanics (76-XX) 34 Mechanics of deformable solids (74-XX) 31 Calculus of variations and optimal control; optimization (49-XX) 26 Differential geometry (53-XX) 22 Biology and other natural sciences (92-XX) 21 Classical thermodynamics, heat transfer (80-XX) 20 Statistical mechanics, structure of matter (82-XX) 6 General and overarching topics; collections (00-XX) 5 Information and communication theory, circuits (94-XX) 4 Ordinary differential equations (34-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Operations research, mathematical programming (90-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Computer science (68-XX) 1 Convex and discrete geometry (52-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

128 Publications have been cited 1,765 times in 884 Documents Cited by Year
On the Cahn-Hilliard equation with degenerate mobility. Zbl 0856.35071
Elliott, Charles M.; Garcke, Harald
1996
Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Zbl 1242.76342
Abels, Helmut; Garcke, Harald; Grün, Günther
2012
On a fourth-order degenerate parabolic equation: Global entropy estimates, existence, and qualitative behavior of solutions. Zbl 0929.35061
Dal Passo, Roberta; Garcke, Harald; Grün, Günther
1998
Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. Zbl 0947.65109
Barrett, John W.; Blowey, James F.; Garcke, Harald
1999
A parametric finite element method for fourth order geometric evolution equations. Zbl 1112.65093
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2007
On anisotropic order parameter models for multi-phase systems and their sharp interface limits. Zbl 0936.82010
Garcke, Harald; Nestler, Britta; Stoth, Barbara
1998
A multiphase field concept: Numerical simulations of moving phase boundaries and multiple junctions. Zbl 0942.35095
Garcke, Harald; Nestler, Britta; Stoth, Barbara
1999
On the parametric finite element approximation of evolving hypersurfaces in $$\mathbb R^3$$. Zbl 1145.65068
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. Zbl 1336.92038
Garcke, Harald; Lam, Kei Fong; Sitka, Emanuel; Styles, Vanessa
2016
Parametric approximation of willmore flow and related geometric evolution equations. Zbl 1186.65133
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
The thin viscous flow equation in higher space dimensions. Zbl 0954.35035
Bertsch, Michiel; Dal Passo, Roberta; Garcke, Harald; Grün, Günther
1998
On Cahn-Hilliard systems with elasticity. Zbl 1130.74037
Garcke, Harald
2003
On fully practical finite element approximations of degenerate Cahn-Hilliard systems. Zbl 0987.35071
Barrett, John W.; Blowey, James F.; Garcke, Harald
2001
Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Zbl 0913.65084
Barrett, John W.; Blowey, James F.; Garcke, Harald
1998
On the variational approximation of combined second and fourth order geometric evolution equations. Zbl 1148.65074
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2007
Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities. Zbl 1273.76421
Abels, Helmut; Depner, Daniel; Garcke, Harald
2013
A singular limit for a system of degenerate Cahn-Hilliard equations. Zbl 0988.35019
Garcke, Harald; Novick-Cohen, Amy
2000
Existence results for diffusive surface motion laws. Zbl 0876.35050
Elliott, Charles M.; Garcke, Harald
1997
Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. Zbl 1375.92011
Garcke, Harald; Lam, Kei Fong
2017
Surfactant spreading on thin viscous films: nonnegative solutions of a coupled degenerate system. Zbl 1102.35056
Garcke, Harald; Wieland, Sandra
2006
A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis. Zbl 1380.92029
Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel
2018
Diffuse interface modelling of soluble surfactants in two-phase flow. Zbl 1319.35309
Garcke, Harald; Lam, Kei Fong; Stinner, Björn
2014
On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. Zbl 1347.76052
Abels, Helmut; Depner, Daniel; Garcke, Harald
2013
On a Cahn–Hilliard model for phase separation with elastic misfit. Zbl 1072.35081
Garcke, Harald
2005
Analysis of a Cahn-Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis. Zbl 1360.35042
Garcke, Harald; Lam, Kei Fong
2017
A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow. Zbl 1329.76168
Garcke, Harald; Hinze, Michael; Kahle, Christian
2016
Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints. Zbl 1272.65060
Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa
2013
The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute. Zbl 1218.65105
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2011
A multi-phase Mullins-Sekerka system: Matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem. Zbl 0924.35199
Bronsard, Lia; Garcke, Harald; Stoth, Barbara
1998
Optimal control of treatment time in a diffuse interface model of tumor growth. Zbl 1403.35139
Garcke, Harald; Lam, Kei Fong; Rocca, Elisabetta
2018
Phase-field approaches to structural topology optimization. Zbl 1356.49044
Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Srisupattarawanit, Tarin; Styles, Vanessa; Voigt, Axel
2012
A diffuse interface model for alloys with multiple components and phases. Zbl 1126.82025
Garcke, Harald; Nestler, Britta; Stinner, Bjorn
2004
Finite element approximation of surfactant spreading on a thin film. Zbl 1130.76361
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2003
The Cahn-Hilliard equation with elasticity – finite element approximation and qualitative studies. Zbl 0972.35164
Garcke, Harald; Rumpf, Martin; Weikard, Ulrich
2001
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 0925.35087
Elliott, Charles M.; Garcke, Harald
1997
A stable numerical method for the dynamics of fluidic membranes. Zbl 1391.76298
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2016
On the stable numerical approximation of two-phase flow with insoluble surfactant. Zbl 1315.35156
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2015
Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis. Zbl 1410.35058
Ebenbeck, Matthias; Garcke, Harald
2019
Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. Zbl 1242.65188
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2012
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies. Zbl 1205.65263
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2010
Allen-Cahn systems with volume constraints. Zbl 1147.49036
Garcke, Harald; Nestler, Britta; Stinner, Björn; Wendler, Frank
2008
Relating phase field and sharp interface approaches to structural topology optimization. Zbl 1301.49113
Blank, Luise; Garcke, Harald; Farshbaf-Shaker, M. Hassan; Styles, Vanessa
2014
Numerical approximation of gradient flows for closed curves in $$\mathbb R^{d}$$. Zbl 1185.65027
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2010
Second order phase field asymptotics for multi-component systems. Zbl 1106.35116
Garcke, Harald; Stinner, Björn
2006
Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid. Zbl 1078.74050
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2006
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix. Zbl 1194.35225
Elliott, Charles M.; Garcke, Harald
1997
Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth. Zbl 1434.35255
Garcke, Harald; Lam, Kei Fong
2016
Stable finite element approximations of two-phase flow with soluble surfactant. Zbl 1349.76175
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2015
Multi-material phase field approach to structural topology optimization. Zbl 1327.49068
Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Rupprecht, Christoph; Styles, Vanessa
2014
On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth. Zbl 1201.80075
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2010
On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms. Zbl 1406.92296
Garcke, Harald; Lam, Kei Fong
2018
Numerical approximation of phase field based shape and topology optimization for fluids. Zbl 1322.35113
Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian
2015
A stable parametric finite element discretization of two-phase Navier-Stokes flow. Zbl 1320.76059
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2015
Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow. Zbl 1286.76040
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2013
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method. Zbl 1233.35132
Blank, Luise; Butz, Martin; Garcke, Harald
2011
Numerical approximation of anisotropic geometric evolution equations in the plane. Zbl 1145.65069
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
A variational formulation of anisotropic geometric evolution equations in higher dimensions. Zbl 1149.65082
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering. Zbl 1410.80015
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2010
Anisotropy in multi-phase systems: A phase field approach. Zbl 0959.35169
Garcke, Harald; Stoth, Barbara; Nestler, Britta
1999
Mean curvature flow with triple junctions in higher space dimensions. Zbl 1291.53078
Depner, Daniel; Garcke, Harald; Kohsaka, Yoshihito
2014
A phase field model for the electromigration of intergranular voids. Zbl 1132.35082
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2007
Numerical approximation of the Cahn-Larché equation. Zbl 1099.74063
Garcke, Harald; Weikard, Ulrich
2005
A coupled surface-Cahn-Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes. Zbl 1338.35222
Garcke, Harald; Kampmann, Johannes; Rätz, Andreas; Röger, Matthias
2016
Finite element approximation of one-sided Stefan problems with anisotropic, approximately crystalline, Gibbs-Thomson law. Zbl 1271.80005
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2013
Elastic flow with junctions: variational approximation and applications to nonlinear splines. Zbl 1252.76038
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2012
Solutions of a fourth order degenerate parabolic equation with weak initial trace. Zbl 0945.35049
Dal Passo, Roberta; Garcke, Harald
1999
Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: a gradient flow approach. Zbl 1429.35114
Garcke, Harald; Knopf, Patrik
2020
On a Cahn-Hilliard-Brinkman model for tumor growth and its singular limits. Zbl 1420.35116
Ebenbeck, Matthias; Garcke, Harald
2019
A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities. Zbl 1394.35353
Dedè, Luca; Garcke, Harald; Lam, Kei Fong
2018
Finite element approximation for the dynamics of asymmetric fluidic biomembranes. Zbl 1394.76064
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2017
Stable numerical approximation of two-phase flow with a Boussinesq-Scriven surface fluid. Zbl 1329.35241
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2015
Curvature driven interface evolution. Zbl 1279.53064
Garcke, Harald
2013
Linearized stability analysis of surface diffusion for hypersurfaces with triple lines. Zbl 1263.35031
Depner, Daniel; Garcke, Harald
2013
Allen-Cahn and Cahn-Hilliard variational inequalities solved with optimization techniques. Zbl 1356.49009
Blank, Luise; Butz, Martin; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa
2012
Linearized stability analysis of stationary solutions for surface diffusion with boundary conditions. Zbl 1097.35030
Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito
2005
A phase-field model for the solidification process in multicomponent alloys. Zbl 1061.80004
Garcke, H.; Nestler, B.; Stinner, B.
2003
A mathematical model for grain growth in thin metallic films. Zbl 1205.74138
Garcke, Harald; Nestler, Britta
2000
Travelling wave solutions as dynamic phase transitions in shape memory alloys. Zbl 0829.73007
Garcke, Harald
1995
Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature. Zbl 1433.65206
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2017
Two-phase flow with surfactants: diffuse interface models and their analysis. Zbl 1391.76766
Abels, Helmut; Garcke, Harald; Lam, Kei Fong; Weber, Josef
2017
Segmentation and restoration of images on surfaces by parametric active contours with topology changes. Zbl 1405.94014
Benninghoff, Heike; Garcke, Harald
2016
A phase field approach for shape and topology optimization in Stokes flow. Zbl 1329.76108
Garcke, Harald; Hecht, Claudia
2015
Efficient image segmentation and restoration using parametric curve evolution with junctions and topology changes. Zbl 1308.94013
Benninghoff, Heike; Garcke, Harald
2014
Nonlocal Allen-Cahn systems. Analysis and a primal-dual active set method. Zbl 1279.65087
Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa
2013
Stress- and diffusion-induced interface motion: modelling and numerical simulations. Zbl 1128.74004
Garcke, Harald; Nürnberg, Robert; Styles, Vanessa
2007
Bi-directional diffusion induced grain boundary motion with triple junctions. Zbl 1081.35116
Garcke, H.; Styles, Vanessa
2004
Willmore flow of planar networks. Zbl 1436.35233
Garcke, Harald; Menzel, Julia; Pluda, Alessandra
2019
Sharp interface limit for a phase field model in structural optimization. Zbl 1348.35259
Blank, Luise; Garcke, Harald; Hecht, Claudia; Rupprecht, Christoph
2016
Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension. Zbl 1335.53079
Abels, Helmut; Garcke, Harald; Müller, Lars
2016
Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biomembranes. Zbl 1210.35258
Farshbaf-Shaker, M. Hassan; Garcke, Harald
2011
Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation. Zbl 1204.35026
Alfaro, Matthieu; Garcke, Harald; Hilhorst, Danielle; Matano, Hiroshi; Schätzle, Reiner
2010
Surface diffusion with triple junctions: A stability criterion for stationary solutions. Zbl 1228.35042
Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito
2010
On sharp interface limits of Allen-Cahn/Cahn-Hilliard variational inequalities. Zbl 1165.35406
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach. Zbl 1352.49046
Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian; Lam, Kei Fong
2016
Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects. Zbl 1428.53104
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2016
Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow. Zbl 1342.35218
Garcke, Harald; Hecht, Claudia
2016
Shape and topology optimization in Stokes flow with a phase field approach. Zbl 1334.49133
Garcke, Harald; Hecht, Claudia
2016
The $$\Gamma$$-limit of the Ginzburg-Landau energy in an elastic medium. Zbl 1193.49054
Garcke, Harald
2008
Nonlinear stability of stationary solutions for surface diffusion with boundary conditions. Zbl 1167.35005
Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito
2008
Mathematical modelling. Zbl 1223.00014
Eck, Christof; Garcke, Harald; Knabner, Peter
2008
On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects. Zbl 1456.35091
Garcke, Harald; Lam, Kei Fong; Signori, Andrea
2021
Weak solutions of the Cahn-Hilliard system with dynamic boundary conditions: a gradient flow approach. Zbl 1429.35114
Garcke, Harald; Knopf, Patrik
2020
Parametric finite element approximations of curvature-driven interface evolutions. Zbl 1455.35185
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2020
On the surface diffusion flow with triple junctions in higher space dimensions. Zbl 1439.53079
Garcke, H.; Gößwein, M.
2020
Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis. Zbl 1410.35058
Ebenbeck, Matthias; Garcke, Harald
2019
On a Cahn-Hilliard-Brinkman model for tumor growth and its singular limits. Zbl 1420.35116
Ebenbeck, Matthias; Garcke, Harald
2019
Willmore flow of planar networks. Zbl 1436.35233
Garcke, Harald; Menzel, Julia; Pluda, Alessandra
2019
Optimal control of time-discrete two-phase flow driven by a diffuse-interface model. Zbl 1437.35575
Garcke, Harald; Hinze, Michael; Kahle, Christian
2019
Variational discretization of axisymmetric curvature flows. Zbl 1419.65051
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2019
A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis. Zbl 1380.92029
Garcke, Harald; Lam, Kei Fong; Nürnberg, Robert; Sitka, Emanuel
2018
Optimal control of treatment time in a diffuse interface model of tumor growth. Zbl 1403.35139
Garcke, Harald; Lam, Kei Fong; Rocca, Elisabetta
2018
On a Cahn-Hilliard-Darcy system for tumour growth with solution dependent source terms. Zbl 1406.92296
Garcke, Harald; Lam, Kei Fong
2018
A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities. Zbl 1394.35353
Dedè, Luca; Garcke, Harald; Lam, Kei Fong
2018
Cahn-Hilliard inpainting with the double obstacle potential. Zbl 1455.94019
Garcke, Harald; Lam, Kei Fong; Styles, Vanessa
2018
Gradient flow dynamics of two-phase biomembranes: sharp interface variational formulation and finite element approximation. Zbl 1416.74070
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2018
A phase field approach to shape optimization in Navier-Stokes flow with integral state constraints. Zbl 1406.35274
Garcke, Harald; Hinze, Michael; Kahle, Christian; Lam, Kei Fong
2018
Well-posedness of a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport. Zbl 1375.92011
Garcke, Harald; Lam, Kei Fong
2017
Analysis of a Cahn-Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis. Zbl 1360.35042
Garcke, Harald; Lam, Kei Fong
2017
Finite element approximation for the dynamics of asymmetric fluidic biomembranes. Zbl 1394.76064
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2017
Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature. Zbl 1433.65206
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2017
Two-phase flow with surfactants: diffuse interface models and their analysis. Zbl 1391.76766
Abels, Helmut; Garcke, Harald; Lam, Kei Fong; Weber, Josef
2017
Finite element approximation for the dynamics of fluidic two-phase biomembranes. Zbl 1383.35153
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2017
Mathematical modeling. Zbl 1386.00063
Eck, Christof; Garcke, Harald; Knabner, Peter
2017
Diffuse interface models for incompressible two-phase flows with different densities. Zbl 1391.76765
Abels, Helmut; Garcke, Harald; Grün, Günther; Metzger, Stefan
2017
Segmentation of three-dimensional images with parametric active surfaces and topology changes. Zbl 1376.65017
Benninghoff, Heike; Garcke, Harald
2017
A Cahn-Hilliard-Darcy model for tumour growth with chemotaxis and active transport. Zbl 1336.92038
Garcke, Harald; Lam, Kei Fong; Sitka, Emanuel; Styles, Vanessa
2016
A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow. Zbl 1329.76168
Garcke, Harald; Hinze, Michael; Kahle, Christian
2016
A stable numerical method for the dynamics of fluidic membranes. Zbl 1391.76298
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2016
Global weak solutions and asymptotic limits of a Cahn-Hilliard-Darcy system modelling tumour growth. Zbl 1434.35255
Garcke, Harald; Lam, Kei Fong
2016
A coupled surface-Cahn-Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes. Zbl 1338.35222
Garcke, Harald; Kampmann, Johannes; Rätz, Andreas; Röger, Matthias
2016
Segmentation and restoration of images on surfaces by parametric active contours with topology changes. Zbl 1405.94014
Benninghoff, Heike; Garcke, Harald
2016
Sharp interface limit for a phase field model in structural optimization. Zbl 1348.35259
Blank, Luise; Garcke, Harald; Hecht, Claudia; Rupprecht, Christoph
2016
Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension. Zbl 1335.53079
Abels, Helmut; Garcke, Harald; Müller, Lars
2016
Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach. Zbl 1352.49046
Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian; Lam, Kei Fong
2016
Computational parametric Willmore flow with spontaneous curvature and area difference elasticity effects. Zbl 1428.53104
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2016
Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow. Zbl 1342.35218
Garcke, Harald; Hecht, Claudia
2016
Shape and topology optimization in Stokes flow with a phase field approach. Zbl 1334.49133
Garcke, Harald; Hecht, Claudia
2016
Image segmentation using parametric contours with free endpoints. Zbl 1408.94048
Benninghoff, Heike; Garcke, Harald
2016
On the stable numerical approximation of two-phase flow with insoluble surfactant. Zbl 1315.35156
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2015
Stable finite element approximations of two-phase flow with soluble surfactant. Zbl 1349.76175
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2015
Numerical approximation of phase field based shape and topology optimization for fluids. Zbl 1322.35113
Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian
2015
A stable parametric finite element discretization of two-phase Navier-Stokes flow. Zbl 1320.76059
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2015
Stable numerical approximation of two-phase flow with a Boussinesq-Scriven surface fluid. Zbl 1329.35241
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2015
A phase field approach for shape and topology optimization in Stokes flow. Zbl 1329.76108
Garcke, Harald; Hecht, Claudia
2015
Stability of spherical caps under the volume-preserving mean curvature flow with line tension. Zbl 1314.53115
Abels, Helmut; Garcke, Harald; Müller, Lars
2015
On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions. Zbl 1366.35006
Abels, Helmut; Arab, Nasrin; Garcke, Harald
2015
Diffuse interface modelling of soluble surfactants in two-phase flow. Zbl 1319.35309
Garcke, Harald; Lam, Kei Fong; Stinner, Björn
2014
Relating phase field and sharp interface approaches to structural topology optimization. Zbl 1301.49113
Blank, Luise; Garcke, Harald; Farshbaf-Shaker, M. Hassan; Styles, Vanessa
2014
Multi-material phase field approach to structural topology optimization. Zbl 1327.49068
Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Rupprecht, Christoph; Styles, Vanessa
2014
Mean curvature flow with triple junctions in higher space dimensions. Zbl 1291.53078
Depner, Daniel; Garcke, Harald; Kohsaka, Yoshihito
2014
Efficient image segmentation and restoration using parametric curve evolution with junctions and topology changes. Zbl 1308.94013
Benninghoff, Heike; Garcke, Harald
2014
Stable phase field approximations of anisotropic solidification. Zbl 1310.65120
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2014
Phase field models versus parametric front tracking methods: are they accurate and computationally efficient? Zbl 1388.65096
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2014
Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities. Zbl 1273.76421
Abels, Helmut; Depner, Daniel; Garcke, Harald
2013
On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility. Zbl 1347.76052
Abels, Helmut; Depner, Daniel; Garcke, Harald
2013
Primal-dual active set methods for Allen-Cahn variational inequalities with nonlocal constraints. Zbl 1272.65060
Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa
2013
Eliminating spurious velocities with a stable approximation of viscous incompressible two-phase Stokes flow. Zbl 1286.76040
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2013
Finite element approximation of one-sided Stefan problems with anisotropic, approximately crystalline, Gibbs-Thomson law. Zbl 1271.80005
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2013
Curvature driven interface evolution. Zbl 1279.53064
Garcke, Harald
2013
Linearized stability analysis of surface diffusion for hypersurfaces with triple lines. Zbl 1263.35031
Depner, Daniel; Garcke, Harald
2013
Nonlocal Allen-Cahn systems. Analysis and a primal-dual active set method. Zbl 1279.65087
Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa
2013
On the stable discretization of strongly anisotropic phase field models with applications to crystal growth. Zbl 1427.74161
Barrett, John. W.; Garcke, Harald; Nürnberg, Robert
2013
Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities. Zbl 1242.76342
Abels, Helmut; Garcke, Harald; Grün, Günther
2012
Phase-field approaches to structural topology optimization. Zbl 1356.49044
Blank, Luise; Garcke, Harald; Sarbu, Lavinia; Srisupattarawanit, Tarin; Styles, Vanessa; Voigt, Axel
2012
Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves. Zbl 1242.65188
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2012
Elastic flow with junctions: variational approximation and applications to nonlinear splines. Zbl 1252.76038
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2012
Allen-Cahn and Cahn-Hilliard variational inequalities solved with optimization techniques. Zbl 1356.49009
Blank, Luise; Butz, Martin; Garcke, Harald; Sarbu, Lavinia; Styles, Vanessa
2012
The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute. Zbl 1218.65105
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2011
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method. Zbl 1233.35132
Blank, Luise; Butz, Martin; Garcke, Harald
2011
Thermodynamically consistent higher order phase field Navier-Stokes models with applications to biomembranes. Zbl 1210.35258
Farshbaf-Shaker, M. Hassan; Garcke, Harald
2011
Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law. Zbl 1235.35286
Garcke, Harald; Schaubeck, Stefan
2011
Mathematical modelling. 2nd revised ed. Zbl 1226.00031
Eck, Christof; Garcke, Harald; Knabner, Peter
2011
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies. Zbl 1205.65263
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2010
Numerical approximation of gradient flows for closed curves in $$\mathbb R^{d}$$. Zbl 1185.65027
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2010
On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth. Zbl 1201.80075
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2010
Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering. Zbl 1410.80015
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2010
Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation. Zbl 1204.35026
Alfaro, Matthieu; Garcke, Harald; Hilhorst, Danielle; Matano, Hiroshi; Schätzle, Reiner
2010
Surface diffusion with triple junctions: A stability criterion for stationary solutions. Zbl 1228.35042
Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito
2010
An anisotropic, inhomogeneous, elastically modified Gibbs-Thomson law as singular limit of a diffuse interface model. Zbl 1233.35010
Garcke, Harald; Kraus, Christiane
2010
Nonlinear stability of stationary solutions for curvature flow with triple junction. Zbl 1187.35013
Garcke, Harald; Kohsaka, Yoshihito; Ševčovič, Daniel
2009
On the parametric finite element approximation of evolving hypersurfaces in $$\mathbb R^3$$. Zbl 1145.65068
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
Parametric approximation of willmore flow and related geometric evolution equations. Zbl 1186.65133
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
Allen-Cahn systems with volume constraints. Zbl 1147.49036
Garcke, Harald; Nestler, Britta; Stinner, Björn; Wendler, Frank
2008
Numerical approximation of anisotropic geometric evolution equations in the plane. Zbl 1145.65069
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
A variational formulation of anisotropic geometric evolution equations in higher dimensions. Zbl 1149.65082
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
On sharp interface limits of Allen-Cahn/Cahn-Hilliard variational inequalities. Zbl 1165.35406
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2008
The $$\Gamma$$-limit of the Ginzburg-Landau energy in an elastic medium. Zbl 1193.49054
Garcke, Harald
2008
Nonlinear stability of stationary solutions for surface diffusion with boundary conditions. Zbl 1167.35005
Garcke, Harald; Ito, Kazuo; Kohsaka, Yoshihito
2008
Mathematical modelling. Zbl 1223.00014
Eck, Christof; Garcke, Harald; Knabner, Peter
2008
Mini-workshop: Mathematics of biological membranes. Abstracts from the mini-workshop held August 31 – September 6, 2008. Zbl 1177.74021
Garcke, Harald (ed.); Niethammer, Barbara (ed.); Peletier, Mark A. (ed.); Röger, Matthias (ed.)
2008
A parametric finite element method for fourth order geometric evolution equations. Zbl 1112.65093
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2007
On the variational approximation of combined second and fourth order geometric evolution equations. Zbl 1148.65074
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2007
A phase field model for the electromigration of intergranular voids. Zbl 1132.35082
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2007
Stress- and diffusion-induced interface motion: modelling and numerical simulations. Zbl 1128.74004
Garcke, Harald; Nürnberg, Robert; Styles, Vanessa
2007
Surfactant spreading on thin viscous films: nonnegative solutions of a coupled degenerate system. Zbl 1102.35056
Garcke, Harald; Wieland, Sandra
2006
Second order phase field asymptotics for multi-component systems. Zbl 1106.35116
Garcke, Harald; Stinner, Björn
2006
Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid. Zbl 1078.74050
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2006
On asymptotic limits of Cahn-Hilliard systems with elastic misfit. Zbl 1366.74055
Garcke, Harald; Kwak, David Jung Chul
2006
Multiscale problems in solidification processes. Zbl 1366.80004
Eck, Christof; Garcke, Harald; Stinner, Björn
2006
On a Cahn–Hilliard model for phase separation with elastic misfit. Zbl 1072.35081
Garcke, Harald
2005
...and 28 more Documents
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#### Cited by 1,167 Authors

 71 Garcke, Harald 34 Nürnberg, Robert 25 Barrett, John W. 21 Abels, Helmut 19 Lam, Kei Fong 16 Kim, Junseok 13 Miranville, Alain M. 13 Nestler, Britta 12 Elliott, Charles M. 12 Grün, Günther 12 Lowengrub, John Samuel 12 Rocca, Elisabetta 11 Kahle, Christian 10 Sun, Shuyu 10 Wise, Steven M. 9 Grasselli, Maurizio 9 Kraus, Christiane 9 Roubíček, Tomáš 9 Stinner, Bjorn 9 Styles, Vanessa 8 Colli, Pierluigi 8 Hinze, Michael 8 Wheeler, Glen E. 8 Winkler, Michael 8 Yang, Xiaofeng 8 Zhu, Peicheng 7 Blank, Luise 7 Du, Qiang 7 Giorgini, Andrea 7 Kou, Jisheng 7 Nochetto, Ricardo Horacio 7 Olshanskii, Maxim A. 7 Voigt, Axel 7 Wang, Cheng 6 Dai, Shibin 6 Dede, Luca 6 Dong, Suchuan 6 Escher, Joachim 6 Frigeri, Sergio 6 Giacomelli, Lorenzo 6 Hughes, Thomas J. R. 6 Lee, Hyun Geun 6 Liu, Chein-Shan 6 Matthes, Daniel 6 Metzger, Stefan 6 Pozzi, Paola 6 Scarpa, Luca 6 Signori, Andrea 6 Stoll, Martin 6 Taranets, Roman M. 6 Tomassetti, Giuseppe 6 Wang, Xiaoming 6 Yang, Zhiguo 6 Zhao, Xiaopeng 5 Aland, Sebastian 5 Alber, Hans-Dieter 5 Bonetti, Elena 5 Bretin, Elie 5 Chugunova, Marina A. 5 Deckelnick, Klaus 5 Fabrizio, Mauro 5 Fischer, Julian 5 Glasner, Karl B. 5 Hecht, Claudia 5 Hintermüller, Michael 5 Jüngel, Ansgar 5 King, John Robert 5 Liang, Bo 5 Lin, Ping 5 Selzer, Michael 5 Shen, Jie 5 Tavakoli, Rouhollah 5 Van Brummelen, Harald 5 Wang, Qi 5 Xu, Yan 5 Zhao, Quan 4 Baňas, L’ubomír 4 Bänsch, Eberhard 4 Bartels, Sören 4 Beneš, Michal 4 Bertozzi, Andrea Louise 4 Bosch, Jessica 4 Boyer, Franck 4 Burger, Martin 4 Calo, Victor Manuel 4 Depner, Daniel 4 Ebenbeck, Matthias 4 Esedoglu, Selim 4 Farshbaf-Shaker, Mohammad Hassan 4 Fukao, Takeshi 4 Gal, Ciprian Gheorghe Sorin 4 Giesselmann, Jan 4 Giorgi, Claudio 4 Gnann, Manuel V. 4 Guo, Ruihan 4 Han, Daozhi 4 Heida, Martin 4 Knabner, Peter 4 Knopf, Patrik 4 Knüpfer, Hans ...and 1,067 more Authors
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#### Cited in 169 Serials

 105 Journal of Computational Physics 34 Computer Methods in Applied Mechanics and Engineering 23 Archive for Rational Mechanics and Analysis 23 Journal of Scientific Computing 23 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 22 Numerische Mathematik 21 Journal of Mathematical Analysis and Applications 20 Journal of Computational and Applied Mathematics 20 Journal of Differential Equations 19 Physica D 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 European Journal of Applied Mathematics 15 SIAM Journal on Mathematical Analysis 15 SIAM Journal on Scientific Computing 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 SIAM Journal on Numerical Analysis 13 Computers & Mathematics with Applications 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 Mathematical Methods in the Applied Sciences 12 Discrete and Continuous Dynamical Systems 11 Nonlinear Analysis. Real World Applications 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Applied Mathematics and Optimization 10 SIAM Journal on Control and Optimization 9 Journal of Fluid Mechanics 9 Mathematics of Computation 9 Applied Mathematics and Computation 9 Applied Numerical Mathematics 9 SIAM Journal on Applied Mathematics 8 Computational Mechanics 8 Calculus of Variations and Partial Differential Equations 8 Advances in Computational Mathematics 7 Journal of Mathematical Physics 7 Communications in Partial Differential Equations 7 Continuum Mechanics and Thermodynamics 7 Interfaces and Free Boundaries 6 Applicable Analysis 6 Nonlinearity 6 Numerical Methods for Partial Differential Equations 6 Applied Mathematics Letters 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Discrete and Continuous Dynamical Systems. Series S 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 NoDEA. Nonlinear Differential Equations and Applications 5 Discrete and Continuous Dynamical Systems. Series B 4 Physica A 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 International Journal for Numerical Methods in Engineering 4 Mathematics and Computers in Simulation 4 Mathematische Nachrichten 4 Applied Mathematical Modelling 4 Journal of Nonlinear Science 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Journal of Mathematical Fluid Mechanics 4 Journal of Evolution Equations 4 Archives of Computational Methods in Engineering 4 Communications on Pure and Applied Analysis 4 Geometric Flows 3 Computers and Fluids 3 International Journal of Engineering Science 3 Journal of Mathematical Biology 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 3 Quarterly of Applied Mathematics 3 Transactions of the American Mathematical Society 3 European Journal of Mechanics. B. Fluids 3 Analysis (München) 3 Computational Geosciences 3 Milan Journal of Mathematics 3 Multiscale Modeling & Simulation 3 Boundary Value Problems 3 Advances in Nonlinear Analysis 2 Computer Physics Communications 2 Communications on Pure and Applied Mathematics 2 Journal of Statistical Physics 2 Bulletin of Mathematical Biology 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 BIT 2 Calcolo 2 Journal für die Reine und Angewandte Mathematik 2 Zeitschrift für Analysis und ihre Anwendungen 2 Mathematical and Computer Modelling 2 Asymptotic Analysis 2 Japan Journal of Industrial and Applied Mathematics 2 Applications of Mathematics 2 Numerical Algorithms 2 International Journal of Computer Mathematics 2 Journal of Elasticity 2 Journal of Mathematical Imaging and Vision 2 Journal of Mathematical Sciences (New York) 2 Computing and Visualization in Science 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Acta Mathematica Sinica. English Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Stochastics and Dynamics 2 SIAM Journal on Applied Dynamical Systems 2 Structural and Multidisciplinary Optimization 2 SIAM Journal on Imaging Sciences 2 Journal of Theoretical Biology ...and 69 more Serials
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#### Cited in 37 Fields

 560 Partial differential equations (35-XX) 342 Numerical analysis (65-XX) 327 Fluid mechanics (76-XX) 162 Mechanics of deformable solids (74-XX) 94 Biology and other natural sciences (92-XX) 91 Calculus of variations and optimal control; optimization (49-XX) 79 Statistical mechanics, structure of matter (82-XX) 67 Differential geometry (53-XX) 62 Classical thermodynamics, heat transfer (80-XX) 25 Dynamical systems and ergodic theory (37-XX) 19 Global analysis, analysis on manifolds (58-XX) 12 Integral equations (45-XX) 12 Optics, electromagnetic theory (78-XX) 10 Operations research, mathematical programming (90-XX) 9 Ordinary differential equations (34-XX) 9 Computer science (68-XX) 8 Operator theory (47-XX) 8 Probability theory and stochastic processes (60-XX) 6 Functional analysis (46-XX) 6 Geophysics (86-XX) 6 Systems theory; control (93-XX) 6 Information and communication theory, circuits (94-XX) 4 Approximations and expansions (41-XX) 3 Combinatorics (05-XX) 3 Statistics (62-XX) 2 Real functions (26-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of particles and systems (70-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX)

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