Edit Profile (opens in new tab) Velázquez, Juan J. L. Compute Distance To: Compute Author ID: velazquez.juan-j-l Published as: Velázquez, J. J. L.; Velázquez, Juan J. L.; Velazquez, J. J. L.; Velazquez, Juan J. L.; Vlázquez, Juan J. L.; Vélazquez, J. J. L.; Velazquez, J. J. L; Velázquez, Juan J. Homepage: http://www.hcm.uni-bonn.de/people/profile/juan-j-velazquez/ External Links: MGP · arXiv · Math-Net.Ru · dblp · GND Documents Indexed: 185 Publications since 1989, including 1 Book 1 Contribution as Editor Co-Authors: 77 Co-Authors with 159 Joint Publications 1,806 Co-Co-Authors all top 5 Co-Authors 22 single-authored 37 Herrero, Miguel Ángel 32 Niethammer, Barbara 12 Escobedo Martínez, Miguel 12 Friedman, Avner 11 Nota, Alessia 10 Hwang, Hyung Ju 8 Stevens, Angela 6 Hu, Bei 5 Cuesta Romero, Carlota Maria 5 Fontelos López, Marco Antonio 5 Herrmann, Michael 4 Bonacini, Marco 4 Kang, Kyungkeun 4 Rendall, Alan D. 4 Sugiyama, Yoshie 3 Andreucci, Daniele 3 James, Richard D. 3 Jang, Juhi 3 Medina, Elena 3 Mischler, Stéphane 3 Pernas-Castaño, Tania 3 Primi, Ivano 3 Throm, Sebastian 3 Winter, Raphael 2 Angenent, Sigurd Bernardus 2 Ferreira, Marina A. 2 Galaktionov, Victor Aleksandrovich 2 Höfer, Richard M. 2 Kierkels, A. H. M. 2 Lacey, Andrew A. 2 Liţcanu, Gabriela 2 Lukkarinen, Jani 2 Oleaga, Gerardo E. 2 Perthame, Benoît 2 Röger, Matthias 1 Aguareles, Maria 1 Alonso-Orán, Diego 1 Biro, Zsolt 1 Bobylev, Alexandre Vasiljévitch 1 Bonilla, Luis Lopez 1 Calle, Maria 1 Carpio, Ana 1 Chapman, Stephen Jonathan 1 Esenturk, Emre 1 Espejo Arenas, Elio Eduardo 1 Espejo, Elio E. 1 Fila, Marek 1 Filippas, Stathis 1 Giunti, Arianna 1 Götz, Ivan G. 1 Helmers, Michael 1 Henseler, Reiner Thorsten 1 Hernando, Pedro J. 1 Herraiz, Luis A. 1 Jang, Jin Woo 1 Jung, Jaewoo 1 Kindelan, Manuel Segura 1 Knüpfer, Hans 1 Laurençot, Philippe 1 Lienstromberg, Christina 1 Logioti, A. 1 Luckhaus, Stephan 1 Macià, Fabricio 1 McLeod, John Bryce 1 Otto, Felix 1 Pego, Robert L. 1 Posashkov, Sergey A. 1 Primicerio, Mario 1 Rindler, Filip 1 Saffirio, Chiara 1 Schwarzacher, Sebastian 1 Seki, Yukihiro 1 Simonella, Sergio 1 Toral, Raúl 1 Ughi, Maura 1 Vela-Pérez, María 1 Winkler, Michael 1 Wrzosek, Dariusz M. all top 5 Serials 17 Archive for Rational Mechanics and Analysis 14 Journal of Differential Equations 12 Communications in Partial Differential Equations 11 Journal of Statistical Physics 8 Communications in Mathematical Physics 6 Transactions of the American Mathematical Society 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 SIAM Journal on Applied Mathematics 5 Nonlinearity 5 Indiana University Mathematics Journal 5 European Journal of Applied Mathematics 5 SIAM Journal on Mathematical Analysis 4 Quarterly of Applied Mathematics 3 Mathematical Methods in the Applied Sciences 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Physica D 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Journal of Nonlinear Science 3 Interfaces and Free Boundaries 3 Kinetic and Related Models 2 Journal of Mathematical Analysis and Applications 2 Journal of Mathematical Biology 2 Mathematische Annalen 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Differential and Integral Equations 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Discrete and Continuous Dynamical Systems 2 Journal of Mathematical Chemistry 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Annales Henri Poincaré 1 Israel Journal of Mathematics 1 Journal of Mathematical Physics 1 Reviews in Mathematical Physics 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Memoirs of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Applied Mathematics Letters 1 Asymptotic Analysis 1 Surveys on Mathematics for Industry 1 Computational Mathematics and Mathematical Physics 1 Journal of Dynamics and Differential Equations 1 Electronic Journal of Differential Equations (EJDE) 1 NoDEA. Nonlinear Differential Equations and Applications 1 Advances in Differential Equations 1 Analysis (München) 1 Discrete and Continuous Dynamical Systems. Series B 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 SIAM Journal on Applied Dynamical Systems 1 Multiscale Modeling & Simulation 1 Oberwolfach Reports 1 Journal of Physics A: Mathematical and Theoretical 1 Networks and Heterogeneous Media 1 Mathematical Modelling of Natural Phenomena 1 Journal of Theoretical Biology 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Fields 145 Partial differential equations (35-XX) 60 Statistical mechanics, structure of matter (82-XX) 32 Fluid mechanics (76-XX) 31 Biology and other natural sciences (92-XX) 27 Integral equations (45-XX) 12 Classical thermodynamics, heat transfer (80-XX) 11 Probability theory and stochastic processes (60-XX) 11 Mechanics of deformable solids (74-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Operator theory (47-XX) 5 Mechanics of particles and systems (70-XX) 4 Ordinary differential equations (34-XX) 3 Numerical analysis (65-XX) 3 Optics, electromagnetic theory (78-XX) 2 Differential geometry (53-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 155 Publications have been cited 2,095 times in 1,319 Documents Cited by ▼ Year ▼ A blow-up mechanism for a chemotaxis model. Zbl 0904.35037Herrero, Miguel A.; Velázquez, Juan J. L. 337 1997 Singularity patterns in a chemotaxis model. Zbl 0864.35008Herrero, Miguel A.; Velázquez, Juan J. L. 114 1996 Chemotactic collapse for the Keller-Segel model. Zbl 0866.92009Herrero, Miguel A.; Velázquez, Juan J. L. 89 1996 Blow-up behaviour of one-dimensional semilinear parabolic equations. Zbl 0813.35007Herrero, M. A.; Velázquez, J. J. L. 70 1993 Blow up of solutions of supercritical semilinear parabolic equations. (Explosion de solutions d’équations paraboliques semilinéaires supercritiques.) Zbl 0806.35005Herrero, Miguel A.; Velázquez, Juan J. L. 63 1994 Finite-time aggregation into a single point in a reaction-diffusion system. Zbl 0909.35071Herrero, M. A.; Medina, E.; Velázquez, J. J. L. 58 1997 Simultaneous finite time blow-up in a two-species model for chemotaxis. Zbl 1186.35098Espejo Arenas, Elio Eduardo; Stevens, Angela; Velázquez, Juan J. L. 53 2009 An integro-differential equation arising as a limit of individual cell-based models. Zbl 1089.45002Bodnar, M.; Velazquez, J. J. L. 49 2006 Liouville theorems and blow up behaviour in semilinear reaction diffusion systems. Zbl 0877.35019Andreucci, D.; Herrero, M. A.; Velázquez, J. J. L. 42 1997 Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity. Zbl 0988.35032Filippas, Stathis; Herrero, Miguel A.; Velázquez, Juan J. L. 41 2000 Point dynamics in a singular limit of the Keller-Segel model. I: Motion of the concentration regions. Zbl 1058.35021Velázquez, J. J. L. 41 2004 Higher dimensional blow up for semilinear parabolic equations. Zbl 0813.35009Velázquez, J. J. L. 39 1992 Classification of singularities for blowing up solutions in higher dimensions. Zbl 0803.35015Velázquez, J. J. L. 37 1993 Estimates on the \((n-1)\)-dimensional Hausdorff measure of the blow-yp set for a semilinear heat equation. Zbl 0802.35073Velázquez, J. J. L. 36 1993 Self-similar blow-up for a reaction-diffusion system. Zbl 0934.35066Herrero, M. A.; Medina, E.; Velázquez, J. J. L. 32 1998 Derivation of macroscopic equations for individual cell-based models: a formal approach. Zbl 1074.60101Bodnar, M.; Velazquez, J. J. L. 32 2005 Blow-up profiles in one-dimensional, semilinear parabolic problems. Zbl 0772.35027Herrero, M. A.; Velázquez, J. J. L. 29 1992 Flat blow-up in one-dimensional semilinear heat equations. Zbl 0767.35036Herrero, M. A.; Velázquez, J. J. L. 29 1992 Degenerate neckpinches in mean curvature flow. Zbl 0866.58055Angenent, S. B.; Velázquez, J. J. L. 29 1997 Finite time blow-up and condensation for the bosonic Nordheim equation. Zbl 1317.35256Escobedo, M.; Velázquez, J. J. L. 26 2015 Measure valued solutions of the 2D Keller-Segel system. Zbl 1256.35180Luckhaus, S.; Sugiyama, Y.; Velázquez, J. J. L. 25 2012 Point dynamics in a singular limit of the Keller-Segel model. II: Formation of the concentration regions. Zbl 1058.35022Velázquez, J. J. L. 24 2004 Approaching an extinction point in one-dimensional semilinear heat equations with strong absorption. Zbl 0799.35111Herrero, M. A.; Velázquez, J. J. L. 22 1992 Generic behaviour of one-dimensional blow up patterns. Zbl 0798.35081Herrero, M. A.; Velázquez, J. J. L. 22 1992 Asymptotic shape of cusp singularities in curve shortening. Zbl 0829.35058Angenent, S. B.; Velázquez, J. J. L. 22 1995 Self-similar solutions with fat tails for Smoluchowski’s coagulation equation with locally bounded kernels. Zbl 1267.82086Niethammer, B.; Velázquez, J. J. L. 22 2013 Singular solutions for the Uehling-Uhlenbeck equation. Zbl 1148.35015Escobedo, M.; Mischler, S.; Velázquez, J. J. L. 19 2008 A note on non-simultaneous blow-up for a drift-diffusion model. Zbl 1240.35230Espejo, E. E.; Stevens, A.; Velázquez, J. J. L. 18 2010 The Becker-Döring equations and the Lifshitz-Slyozov theory of coarsening. Zbl 0963.82036Velázquez, J. J. L. 17 1998 Global existence for the Vlasov-Poisson system in bounded domains. Zbl 1218.35235Hwang, Hyung Ju; Velázquez, Juan J. L. 17 2010 The method of reflections, homogenization and screening for Poisson and Stokes equations in perforated domains. Zbl 1384.35089Höfer, Richard M.; Velázquez, Juan J. L. 16 2018 On the blow up and condensation of supercritical solutions of the Nordheim equation for bosons. Zbl 1294.35166Escobedo, M.; Velázquez, J. J. L. 16 2014 Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data. Zbl 1228.35252Hwang, Hyung Ju; Rendall, Alan D.; Velázquez, Juan J. L. 16 2011 On the existence of exponentially decreasing solutions of the nonlinear Landau damping problem. Zbl 1193.35229Hwang, Hyung Ju; Velazquez, Juan J. L. 16 2009 A nonlinear Fokker-Planck equation modelling the approach to thermal equilibrium in a homogeneous plasma. Zbl 0933.35090Escobedo, M.; Herrero, M. A.; Velazquez, J. J. L. 15 1998 On the fundamental solution of a linearized Uehling-Uhlenbeck equation. Zbl 1387.35105Escobedo, M.; Mischler, S.; Vélazquez, J. J. L. 15 2007 On global existence for the Vlasov-Poisson system in a half space. Zbl 1181.35291Hwang, Hyung Ju; Velázquez, Juan J. L. 15 2009 On the melting of ice balls. Zbl 0876.35137Herrero, Miguel A.; Velázquez, Juan J. L. 15 1997 Stability of some mechanisms of chemotactic aggregation. Zbl 1013.35004Velázquez, J. J. L. 14 2002 On the dynamics of a semilinear heat equation with strong absorption. Zbl 0697.35019Herrero, M. A.; Velázquez, J. J. L. 13 1989 Global existence for reaction-diffusion systems modelling ignition. Zbl 0909.35063Herrero, Miguel A.; Lacey, Andrew A.; Velázquez, Juan J. L. 12 1998 The Fokker-Planck equation with absorbing boundary conditions. Zbl 1305.35147Hwang, Hyung Ju; Jang, Juhi; Velázquez, Juan J. L. 12 2014 A Stefan problem for a protocell model with symmetry-breaking bifurcations of analytic solutions. Zbl 0994.35124Friedman, Avner; Hu, Bei; Velazquez, Juan J. L. 12 2001 Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes. Zbl 1448.60136Giunti, Arianna; Höfer, Richard; Velázquez, Juan J. L. 11 2018 Self-similar solutions with fat tails for Smoluchowski’s coagulation equation with singular kernels. (Solutions auto-similaire avec queues lourdes pour l’équation de coagulation de Smoluchowski avec noyaux singuliers.) Zbl 1357.35073Niethammer, B.; Throm, S.; Velázquez, J. J. L. 11 2016 An integro-differential equation model for alignment and orientational aggregation. Zbl 1157.47054Kang, Kyungkeun; Perthame, Benoit; Stevens, Angela; Velázquez, J. J. L. 11 2009 Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow. Zbl 0926.35023Velázquez, J. J. L. 10 1994 Local behaviour near blow-up points for semilinear parabolic equations. Zbl 0798.35023Velázquez, J. J. L. 10 1993 Screening in interacting particle systems. Zbl 1113.82049Niethammer, B.; Velázquez, J. J. L. 10 2006 Qualitative behavior of a Keller-Segel model with non-diffusive memory. Zbl 1193.35013Kang, Kyungkeun; Stevens, Angela; Velázquez, Juan J. L. 9 2010 Asymptotic description of Dirac mass formation in kinetic equations for quantum particles. Zbl 1072.35160Escobedo, M.; Mischler, S.; Velazquez, J. J. L. 9 2004 Friction dominated dynamics of interacting particles locally close to a crystallographic lattice. Zbl 1275.35123Bodnar, M.; Velázquez, J. J. L. 9 2013 Well-posedness of a model of point dynamics for a limit of the Keller-Segel system. Zbl 1063.35068Velázquez, J. J. L. 8 2004 Exponential tail behavior of self-similar solutions to Smoluchowski’s coagulation equation. Zbl 1307.45011Niethammer, B.; Velázquez, J. J. L. 8 2014 On the theory of weak turbulence for the nonlinear Schrödinger equation. Zbl 1329.35278Escobedo, M.; Velázquez, J. J. L. 8 2015 Singularity formation in the one-dimensional supercooled Stefan problem. Zbl 0855.35135Herrero, Miguel A.; Velázquez, Juan J. L. 8 1996 Some results on blow up for semilinear parabolic problems. Zbl 0828.35056Herrero, M. A.; Velázquez, J. J. L. 8 1993 Optimal bounds for self-similar solutions to coagulation equations with product kernel. Zbl 1235.45009Niethammer, B.; Velázquez, J. J. L. 8 2011 On the convergence to the smooth self-similar solution in the LSW model. Zbl 1098.35032Niethammer, B.; Velázquez, J. J. L. 8 2006 Oscillatory dynamics in Smoluchowski’s coagulation equation with diagonal kernel. Zbl 1407.82039Laurençot, Philippe; Niethammer, Barbara; Velázquez, Juan J. L. 7 2018 Uniqueness of self-similar solutions to Smoluchowski’s coagulation equations for kernels that are close to constant. Zbl 1302.82136Niethammer, B.; Velázquez, J. J. L. 7 2014 Sol-gel transition in a coagulation-diffusion model. Zbl 1033.82011Herrero, M. A.; Velázquez, J. J. L.; Wrzosek, D. 7 2000 Instabilities and oscillations in coagulation equations with kernels of homogeneity one. Zbl 1404.82042Herrmann, Michael; Niethammer, Barbara; Velázquez, Juan J. L. 7 2017 A uniqueness result for self-similar profiles to Smoluchowski’s coagulation equation revisited. Zbl 1356.82034Niethammer, B.; Throm, S.; Velázquez, J. J. L. 7 2016 On the transfer of energy towards infinity in the theory of weak turbulence for the nonlinear Schrödinger equation. Zbl 1331.35256Kierkels, A. H. M.; Velázquez, J. J. L. 7 2015 Self-similar profiles for homoenergetic solutions of the Boltzmann equation: particle velocity distribution and entropy. Zbl 1430.82012James, Richard D.; Nota, Alessia; Velázquez, Juan J. L. 6 2019 Global stability and bounds for coarsening rates within the mean-field theory for domain coarsening. Zbl 1113.35029Niethammer, B.; Velázquez, J. J. L. 6 2006 Mass-selection in alignment models with non-deterministic effects. Zbl 1169.82022Primi, I.; Stevens, A.; Velázquez, J. J. L. 6 2009 The evolution of stress intensity factors and the propagation of cracks in elastic media. Zbl 0970.74058Friedman, Avner; Hu, Bei; Velazquez, Juan J. L. 6 2000 On the effect of stochastic fluctuations in the dynamics of the Lifshitz-Slyozov-Wagner model. Zbl 0973.82029Velázquez, J. J. L. 6 2000 A class of dust-like self-similar solutions of the massless Einstein-Vlasov system. Zbl 1216.83066Rendall, Alan D.; Velázquez, Juan J. L. 6 2011 On the fundamental solution of a linearized homogeneous coagulation equation. Zbl 1193.82061Escobedo, Miguel; Velázquez, J. J. L. 6 2010 Homogenization in coarsening systems. I: Deterministic case. Zbl 1082.35023Niethammer, B.; Velázquez, J. J. L. 6 2004 Blow-up rate estimates for the solutions of the bosonic Boltzmann-Nordheim equation. Zbl 1320.35249Bandyopadhyay, J.; Velázquez, J. J. L. 6 2015 Plane structures in thermal runaway. Zbl 0813.35035Herrero, M. A.; Velázquez, J. J. L. 6 1993 The two-particle correlation function for systems with long-range interactions. Zbl 1400.82176Velázquez, Juan J. L.; Winter, Raphael 5 2018 On the theory of Lorentz gases with long range interactions. Zbl 1393.82019Nota, Alessia; Simonella, Sergio; Velázquez, Juan J. L. 5 2018 Comportement générique au voisinage d’un point d’explosion pour des solutions d’équations paraboliques unidimensionnelles. (Generic blow-up behaviour of solutions of one-dimensional semilinear parabolic problems). Zbl 0765.35009Herrero, Miguel A.; Velázquez, Juan J. L. 5 1992 Self-similar blow up with a continuous range of values of the aggregated mass for a degenerate Keller-Segel system. Zbl 1221.35087Sugiyama, Y.; Velázquez, J. J. L. 5 2011 Global well-posedness for an inhomogeneous LSW-model in unbounded domains. Zbl 1206.82071Niethammer, B.; Velázquez, J. J. L. 5 2004 Approaching a vertex in a shrinking domain under a nonlinear flow. Zbl 1064.35085Herrero, M. A.; Ughi, M.; Velázquez, J. J. L. 5 2004 The analysis of coating flows near the contact line. Zbl 0851.35106Friedman, Avner; Velázquez, Juan J. L. 5 1995 Stability analysis of a closed thermosyphon. Zbl 0701.76086Herrero, M. A.; Velazquez, J. J. L 5 1990 Kramers and non-Kramers phase transitions in many-particle systems with dynamical constraint. Zbl 1255.35209Herrmann, Michael; Niethammer, Barbara; Velázquez, Juan J. L. 5 2012 Blow up for semilinear parabolic equations. Zbl 0798.35072Velazquez, Juan J. L. 5 1993 On the dynamics of a closed thermosyphon. Zbl 0823.35151Velázquez, J. J. L. 5 1994 Partial differential equations and non-diffusive structures. Zbl 1160.35302Stevens, A.; Velázquez, J. J. L. 5 2008 Self-similar asymptotic behavior for the solutions of a linear coagulation equation. Zbl 1415.35049Niethammer, Barbara; Nota, Alessia; Throm, Sebastian; Velázquez, Juan J. L. 4 2019 On self-similar solutions to a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation. Zbl 1348.35237Kierkels, A. H. M.; Velázquez, J. J. L. 4 2016 Global solutions to a chemotaxis system with non-diffusive memory. Zbl 1333.92014Sugiyama, Y.; Tsutsui, Y.; Velázquez, J. J. L. 4 2014 A note on the dissolution of spherical crystals. Zbl 0979.35147Herraiz, Luis A.; Herrero, Miguel A.; Velázquez, Juan J. L. 4 2001 Self-similar solutions with fat tails for a coagulation equation with diagonal kernel. Zbl 1219.35031Niethammer, Barbara; Velázquez, Juan J. L. 4 2011 Asymptotics of self-similar solutions to coagulation equations with product kernel. Zbl 1229.82125McLeod, J. B.; Niethammer, B.; Velázquez, J. J. L. 4 2011 Homogenization in coarsening systems. II: Stochastic case. Zbl 1068.35171Niethammer, B.; Velázquez, J. J. L. 4 2004 The analysis of coating flows in a strip. Zbl 0836.76022Friedman, Avner; Velázquez, Juan J. L. 4 1995 Multiple peak aggregations for the Keller-Segel system. Zbl 1282.35098Seki, Yukihiro; Sugiyama, Yoshie; Velázquez, Juan J. L. 4 2013 Pattern forming instabilities driven by non-diffusive interactions. Zbl 1270.35300Primi, Ivano; Stevens, Angela; Velázquez, Juan J. L. 4 2013 On screening induced fluctuations in Ostwald ripening. Zbl 1139.82027Niethammer, B.; Velázquez, J. J. L. 4 2008 On the growth of a particle coalescing in a Poisson distribution of obstacles. Zbl 1372.82031Nota, Alessia; Velázquez, Juan J. L. 4 2017 Long-time asymptotics for homoenergetic solutions of the Boltzmann equation: collision-dominated case. Zbl 1453.35133James, Richard D.; Nota, Alessia; Velázquez, Juan J. L. 3 2019 Large time behavior of exchange-driven growth. Zbl 1462.34035Esentürk, Emre; Velazquez, Juan 1 2021 Two-speed solutions to non-convex rate-independent systems. Zbl 1460.35016Rindler, Filip; Schwarzacher, Sebastian; Velázquez, Juan J. L. 1 2021 Stationary non-equilibrium solutions for coagulation systems. Zbl 1465.45009Ferreira, Marina A.; Lukkarinen, Jani; Nota, Alessia; Velázquez, Juan J. L. 1 2021 Solutions with peaks for a coagulation-fragmentation equation. I: Stability of the tails. Zbl 1441.35044Bonacini, Marco; Niethammer, Barbara; Velázquez, Juan J. L. 2 2020 A bulk-surface reaction-diffusion system for cell polarization. Zbl 1439.35577Niethammer, Barbara; Röger, Matthias; Velázquez, Juan J. L. 2 2020 Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case. Zbl 1440.35229James, Richard D.; Nota, Alessia; Velázquez, Juan J. L. 2 2020 Analysis of a thin film approximation for two-fluid Taylor-Couette flows. Zbl 1433.76018Pernas-Castaño, Tania; Velázquez, Juan J. L. 2 2020 Temporal oscillations in Becker-Döring equations with atomization. Zbl 1444.34065Pego, Robert L.; Velázquez, Juan J. L. 1 2020 Self-similar asymptotics for a modified Maxwell-Boltzmann equation in systems subject to deformations. Zbl 1454.82032Bobylev, Alexander; Nota, Alessia; Velázquez, Juan J. L. 1 2020 Self-similar profiles for homoenergetic solutions of the Boltzmann equation: particle velocity distribution and entropy. Zbl 1430.82012James, Richard D.; Nota, Alessia; Velázquez, Juan J. L. 6 2019 Self-similar asymptotic behavior for the solutions of a linear coagulation equation. Zbl 1415.35049Niethammer, Barbara; Nota, Alessia; Throm, Sebastian; Velázquez, Juan J. L. 4 2019 Long-time asymptotics for homoenergetic solutions of the Boltzmann equation: collision-dominated case. Zbl 1453.35133James, Richard D.; Nota, Alessia; Velázquez, Juan J. L. 3 2019 Nonuniqueness for the kinetic Fokker-Planck equation with inelastic boundary conditions. Zbl 1408.35190Hwang, Hyung Ju; Jang, Juhi; Velázquez, Juan J. L. 2 2019 Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity one. Zbl 1441.45010Bonacini, Marco; Niethammer, Barbara; Velázquez, Juan J. L. 2 2019 On the structure of the singular set for the kinetic Fokker-Planck equations in domains with boundaries. Zbl 1404.35446Hwang, Hyung Ju; Jang, Juhi; Velázquez, Juan J. L. 2 2019 The method of reflections, homogenization and screening for Poisson and Stokes equations in perforated domains. Zbl 1384.35089Höfer, Richard M.; Velázquez, Juan J. L. 16 2018 Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes. Zbl 1448.60136Giunti, Arianna; Höfer, Richard; Velázquez, Juan J. L. 11 2018 Oscillatory dynamics in Smoluchowski’s coagulation equation with diagonal kernel. Zbl 1407.82039Laurençot, Philippe; Niethammer, Barbara; Velázquez, Juan J. L. 7 2018 The two-particle correlation function for systems with long-range interactions. Zbl 1400.82176Velázquez, Juan J. L.; Winter, Raphael 5 2018 On the theory of Lorentz gases with long range interactions. Zbl 1393.82019Nota, Alessia; Simonella, Sergio; Velázquez, Juan J. L. 5 2018 From a non-Markovian system to the Landau equation. Zbl 1433.60067Velázquez, Juan J. L.; Winter, Raphael 1 2018 Instabilities and oscillations in coagulation equations with kernels of homogeneity one. Zbl 1404.82042Herrmann, Michael; Niethammer, Barbara; Velázquez, Juan J. L. 7 2017 On the growth of a particle coalescing in a Poisson distribution of obstacles. Zbl 1372.82031Nota, Alessia; Velázquez, Juan J. L. 4 2017 Veiled singularities for the spherically symmetric massless Einstein-Vlasov system. Zbl 1381.83049Rendall, Alan D.; Velázquez, Juan J. L. 2 2017 Self-similar solutions with fat tails for Smoluchowski’s coagulation equation with singular kernels. (Solutions auto-similaire avec queues lourdes pour l’équation de coagulation de Smoluchowski avec noyaux singuliers.) Zbl 1357.35073Niethammer, B.; Throm, S.; Velázquez, J. J. L. 11 2016 A uniqueness result for self-similar profiles to Smoluchowski’s coagulation equation revisited. Zbl 1356.82034Niethammer, B.; Throm, S.; Velázquez, J. J. L. 7 2016 On self-similar solutions to a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation. Zbl 1348.35237Kierkels, A. H. M.; Velázquez, J. J. L. 4 2016 Mathematical analysis of a coarsening model with local interactions. Zbl 1379.70046Helmers, Michael; Niethammer, Barbara; Velázquez, Juan J. L. 1 2016 Finite time blow-up and condensation for the bosonic Nordheim equation. Zbl 1317.35256Escobedo, M.; Velázquez, J. J. L. 26 2015 On the theory of weak turbulence for the nonlinear Schrödinger equation. Zbl 1329.35278Escobedo, M.; Velázquez, J. J. L. 8 2015 On the transfer of energy towards infinity in the theory of weak turbulence for the nonlinear Schrödinger equation. Zbl 1331.35256Kierkels, A. H. M.; Velázquez, J. J. L. 7 2015 Blow-up rate estimates for the solutions of the bosonic Boltzmann-Nordheim equation. Zbl 1320.35249Bandyopadhyay, J.; Velázquez, J. J. L. 6 2015 On the blow up and condensation of supercritical solutions of the Nordheim equation for bosons. Zbl 1294.35166Escobedo, M.; Velázquez, J. J. L. 16 2014 The Fokker-Planck equation with absorbing boundary conditions. Zbl 1305.35147Hwang, Hyung Ju; Jang, Juhi; Velázquez, Juan J. L. 12 2014 Exponential tail behavior of self-similar solutions to Smoluchowski’s coagulation equation. Zbl 1307.45011Niethammer, B.; Velázquez, J. J. L. 8 2014 Uniqueness of self-similar solutions to Smoluchowski’s coagulation equations for kernels that are close to constant. Zbl 1302.82136Niethammer, B.; Velázquez, J. J. L. 7 2014 Global solutions to a chemotaxis system with non-diffusive memory. Zbl 1333.92014Sugiyama, Y.; Tsutsui, Y.; Velázquez, J. J. L. 4 2014 Dynamical properties of models for the Calvin cycle. Zbl 1345.92069Rendall, Alan D.; Velázquez, Juan J. L. 2 2014 Rate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control. Zbl 1304.35696Herrmann, Michael; Niethammer, Barbara; Velázquez, Juan J. L. 2 2014 Self-similar solutions with fat tails for Smoluchowski’s coagulation equation with locally bounded kernels. Zbl 1267.82086Niethammer, B.; Velázquez, J. J. L. 22 2013 Friction dominated dynamics of interacting particles locally close to a crystallographic lattice. Zbl 1275.35123Bodnar, M.; Velázquez, J. J. L. 9 2013 Multiple peak aggregations for the Keller-Segel system. Zbl 1282.35098Seki, Yukihiro; Sugiyama, Yoshie; Velázquez, Juan J. L. 4 2013 Pattern forming instabilities driven by non-diffusive interactions. Zbl 1270.35300Primi, Ivano; Stevens, Angela; Velázquez, Juan J. L. 4 2013 Ant foraging and geodesic paths in labyrinths: analytical and computational results. Zbl 1406.92728Vela-Pérez, M.; Fontelos, Marco A.; Velázquez, J. J. L. 3 2013 Bistable stochastic biochemical networks: highly specific systems with few chemicals. Zbl 1320.92043Hwang, Hyung Ju; Velázquez, Juan J. L. 2 2013 On global existence of classical solutions for the Vlasov-Poisson system in convex bounded domains. Zbl 1271.82026Hwang, Hyung Ju; Jung, Jaewoo; Velázquez, Juan J. L. 1 2013 Fluid accumulation in thin-film flows driven by surface tension and gravity. Zbl 1262.76012Cuesta, C. M.; Velázquez, J. J. L. 1 2013 Local well posedness for a linear coagulation equation. Zbl 1316.45010Escobedo, M.; Velázquez, J. J. L. 1 2013 A 2D-model of cell sorting induced by propagation of chemical signals along spiral waves. Zbl 1479.35520Kang, K.; Primi, I.; Velázquez, J. J. L. 1 2013 Bistable stochastic biochemical networks: large chemical networks and systems with many molecules. Zbl 1320.92040Hwang, Hyung Ju; Velázquez, Juan J. L. 1 2013 Measure valued solutions of the 2D Keller-Segel system. Zbl 1256.35180Luckhaus, S.; Sugiyama, Y.; Velázquez, J. J. L. 25 2012 Kramers and non-Kramers phase transitions in many-particle systems with dynamical constraint. Zbl 1255.35209Herrmann, Michael; Niethammer, Barbara; Velázquez, Juan J. L. 5 2012 Analysis of oscillations in a drainage equation. Zbl 1261.37034Cuesta, C. M.; Velázquez, J. J. L. 2 2012 Classical non-mass-preserving solutions of coagulation equations. Zbl 1251.35082Escobedo, M.; Velázquez, J. J. L. 1 2012 The structure of the quiescent core in rigidly rotating spirals in a class of excitable systems. Zbl 1247.35178Aguareles, Maria; Fontelos, Marco A.; Velázquez, Juan J. 1 2012 Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data. Zbl 1228.35252Hwang, Hyung Ju; Rendall, Alan D.; Velázquez, Juan J. L. 16 2011 Optimal bounds for self-similar solutions to coagulation equations with product kernel. Zbl 1235.45009Niethammer, B.; Velázquez, J. J. L. 8 2011 A class of dust-like self-similar solutions of the massless Einstein-Vlasov system. Zbl 1216.83066Rendall, Alan D.; Velázquez, Juan J. L. 6 2011 Self-similar blow up with a continuous range of values of the aggregated mass for a degenerate Keller-Segel system. Zbl 1221.35087Sugiyama, Y.; Velázquez, J. J. L. 5 2011 Self-similar solutions with fat tails for a coagulation equation with diagonal kernel. Zbl 1219.35031Niethammer, Barbara; Velázquez, Juan J. L. 4 2011 Asymptotics of self-similar solutions to coagulation equations with product kernel. Zbl 1229.82125McLeod, J. B.; Niethammer, B.; Velázquez, J. J. L. 4 2011 A note on non-simultaneous blow-up for a drift-diffusion model. Zbl 1240.35230Espejo, E. E.; Stevens, A.; Velázquez, J. J. L. 18 2010 Global existence for the Vlasov-Poisson system in bounded domains. Zbl 1218.35235Hwang, Hyung Ju; Velázquez, Juan J. L. 17 2010 Qualitative behavior of a Keller-Segel model with non-diffusive memory. Zbl 1193.35013Kang, Kyungkeun; Stevens, Angela; Velázquez, Juan J. L. 9 2010 On the fundamental solution of a linearized homogeneous coagulation equation. Zbl 1193.82061Escobedo, Miguel; Velázquez, J. J. L. 6 2010 Simultaneous finite time blow-up in a two-species model for chemotaxis. Zbl 1186.35098Espejo Arenas, Elio Eduardo; Stevens, Angela; Velázquez, Juan J. L. 53 2009 On the existence of exponentially decreasing solutions of the nonlinear Landau damping problem. Zbl 1193.35229Hwang, Hyung Ju; Velazquez, Juan J. L. 16 2009 On global existence for the Vlasov-Poisson system in a half space. Zbl 1181.35291Hwang, Hyung Ju; Velázquez, Juan J. L. 15 2009 An integro-differential equation model for alignment and orientational aggregation. Zbl 1157.47054Kang, Kyungkeun; Perthame, Benoit; Stevens, Angela; Velázquez, J. J. L. 11 2009 Mass-selection in alignment models with non-deterministic effects. Zbl 1169.82022Primi, I.; Stevens, A.; Velázquez, J. J. L. 6 2009 Self-similar solutions for the LSW model with encounters. Zbl 1182.45004Herrmann, M.; Niethammer, B.; Velázquez, J. J. L. 3 2009 Singular solutions for the Uehling-Uhlenbeck equation. Zbl 1148.35015Escobedo, M.; Mischler, S.; Velázquez, J. J. L. 19 2008 Partial differential equations and non-diffusive structures. Zbl 1160.35302Stevens, A.; Velázquez, J. J. L. 5 2008 On screening induced fluctuations in Ostwald ripening. Zbl 1139.82027Niethammer, B.; Velázquez, J. J. L. 4 2008 A kinetic model for grain growth. Zbl 1155.35314Henseler, Reiner; Herrmann, Michael; Niethammer, Barbara; Velázquez, Juan J. L. 3 2008 A derivation of a new set of equations at the onset of the Bose-Einstein condensation. Zbl 1149.82019Escobedo, Miguel; Velázquez, J. J. L. 2 2008 On the fundamental solution of a linearized Uehling-Uhlenbeck equation. Zbl 1387.35105Escobedo, M.; Mischler, S.; Vélazquez, J. J. L. 15 2007 An integro-differential equation arising as a limit of individual cell-based models. Zbl 1089.45002Bodnar, M.; Velazquez, J. J. L. 49 2006 Screening in interacting particle systems. Zbl 1113.82049Niethammer, B.; Velázquez, J. J. L. 10 2006 On the convergence to the smooth self-similar solution in the LSW model. Zbl 1098.35032Niethammer, B.; Velázquez, J. J. L. 8 2006 Global stability and bounds for coarsening rates within the mean-field theory for domain coarsening. Zbl 1113.35029Niethammer, B.; Velázquez, J. J. L. 6 2006 On the effect of correlations, fluctuations and collisions in Ostwald ripening. Zbl 1366.82040Niethammer, Barbara; Otto, Felix; Velázquez, Juan J. L. 3 2006 Singular solutions of partial differential equations modelling chemotactic aggregation. Zbl 1125.35049Velázquez, Juan J. L. 2 2006 Derivation of macroscopic equations for individual cell-based models: a formal approach. Zbl 1074.60101Bodnar, M.; Velazquez, J. J. L. 32 2005 Grow-up on the boundary for a semilinear parabolic problem. Zbl 1090.35034Fila, Marek; Velázquez, Juan J. L.; Winkler, Michael 3 2005 Point dynamics in a singular limit of the Keller-Segel model. I: Motion of the concentration regions. Zbl 1058.35021Velázquez, J. J. L. 41 2004 Point dynamics in a singular limit of the Keller-Segel model. II: Formation of the concentration regions. Zbl 1058.35022Velázquez, J. J. L. 24 2004 Asymptotic description of Dirac mass formation in kinetic equations for quantum particles. Zbl 1072.35160Escobedo, M.; Mischler, S.; Velazquez, J. J. L. 9 2004 Well-posedness of a model of point dynamics for a limit of the Keller-Segel system. Zbl 1063.35068Velázquez, J. J. L. 8 2004 Homogenization in coarsening systems. I: Deterministic case. Zbl 1082.35023Niethammer, B.; Velázquez, J. J. L. 6 2004 Global well-posedness for an inhomogeneous LSW-model in unbounded domains. Zbl 1206.82071Niethammer, B.; Velázquez, J. J. L. 5 2004 Approaching a vertex in a shrinking domain under a nonlinear flow. Zbl 1064.35085Herrero, M. A.; Ughi, M.; Velázquez, J. J. L. 5 2004 Homogenization in coarsening systems. II: Stochastic case. Zbl 1068.35171Niethammer, B.; Velázquez, J. J. L. 4 2004 On the growth of filamentary structures in planar media. Zbl 1058.35101Andreucci, D.; Herrero, M. A.; Velázquez, J. J. L. 3 2004 Planar cracks running along piecewise linear paths. Zbl 1041.74062Herrero, M. A.; Oleaga, G. E.; Velázquez, J. J. L. 1 2004 Stability of some mechanisms of chemotactic aggregation. Zbl 1013.35004Velázquez, J. J. L. 14 2002 Asymptotic behaviour \((t\to +0)\) of the interface for the critical case of undercooled Stefan problem. Zbl 1170.80323Primicerio, Mario; Götz, Ivan G.; Velázquez, Juan J. L. 1 2002 A Stefan problem for a protocell model with symmetry-breaking bifurcations of analytic solutions. Zbl 0994.35124Friedman, Avner; Hu, Bei; Velazquez, Juan J. L. 12 2001 A note on the dissolution of spherical crystals. Zbl 0979.35147Herraiz, Luis A.; Herrero, Miguel A.; Velázquez, Juan J. L. 4 2001 The classical one-phase Stefan problem: a catalog of interface behaviors. Zbl 1048.76058Andreucci, Daniele; Herrero, Miguel A.; Velázquez, Juan J. L. 3 2001 ...and 55 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,287 Authors 81 Velázquez, Juan J. L. 79 Winkler, Michael 31 Niethammer, Barbara 29 Zaag, Hatem 27 Tao, Youshan 26 Mu, Chunlai 25 Carrillo de la Plata, José Antonio 24 Mizoguchi, Noriko 21 Herrero, Miguel Ángel 17 Hwang, Hyung Ju 17 Laurençot, Philippe 15 Souplet, Philippe 14 Galaktionov, Victor Aleksandrovich 13 Escobedo Martínez, Miguel 12 Bertozzi, Andrea Louise 12 Merle, Frank 12 Ren, Guoqiang 12 Zheng, Jiashan 11 Lankeit, Johannes 11 Zheng, Pan 11 Zheng, Sining 10 Bedrossian, Jacob 10 Fujishima, Yohei 10 Ishige, Kazuhiro 10 Lin, Ke 10 Nguyen, Van Tien 10 Nota, Alessia 10 Sugiyama, Yoshie 10 Wang, Liangchen 10 Wang, Yifu 9 Del Pino, Manuel A. 9 Laurent, Thomas 9 Li, Dan 9 Li, Xie 9 Shen, Wenxian 9 Suzuki, Takashi 9 Wang, Wei 8 Cieślak, Tomasz 8 Fetecau, Razvan C. 8 Harada, Junichi 8 Jin, Hai-Yang 8 Kang, Kyungkeun 8 Lu, Xuguang 8 Masmoudi, Nader 8 Nagai, Toshitaka 8 Perthame, Benoît 8 Raphael, Pierre 8 Senba, Takasi 8 Skubachevskiĭ, Aleksandr Leonidovich 8 Tran, Minh-Binh 8 Yokota, Tomomi 7 Collot, Charles 7 Conlon, Joseph G. 7 Fontelos López, Marco Antonio 7 Friedman, Avner 7 Fujie, Kentarou 7 Ghoul, Tej-Eddine 7 Höfer, Richard M. 7 Li, Yuxiang 7 Rossi, Julio Daniel 7 Throm, Sebastian 7 Wang, Yilong 7 Wang, Zhian 7 Xiang, Zhaoyin 6 Biler, Piotr 6 Calvez, Vincent 6 Cao, Xinru 6 Chertock, Alina E. 6 King, John Robert 6 Kurganov, Alexander 6 Nouri, Anne 6 Stinner, Christian 6 Vazquez, Juan Luis 6 Wei, Juncheng 5 Fuest, Mario 5 Gang, Zhou 5 Giunti, Arianna 5 Hillairet, Matthieu 5 Hillen, Thomas 5 Horstmann, Dirk 5 Ishida, Sachiko 5 Issa, Tahir Bachar 5 Liu, Jianguo 5 Liu, Zhengrong 5 McCue, Scott William 5 Osaki, Koichi 5 Pego, Robert L. 5 Salako, Rachidi Bolaji 5 Seki, Yukihiro 5 Sigal, Israel Michael 5 Stevens, Angela 5 Vauchelet, Nicolas 5 Yao, Yao 4 Andréasson, Håkan 4 Arkeryd, Leif O. 4 Bellomo, Nicola 4 Bian, Shen 4 Budd, Christopher John 4 Cañizo, José Alfredo 4 Ding, Mengyao ...and 1,187 more Authors all top 5 Cited in 214 Serials 120 Journal of Differential Equations 75 Journal of Mathematical Analysis and Applications 62 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 43 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 37 Archive for Rational Mechanics and Analysis 36 Journal of Statistical Physics 32 ZAMP. Zeitschrift für angewandte Mathematik und Physik 31 Discrete and Continuous Dynamical Systems 30 Communications in Mathematical Physics 27 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 27 SIAM Journal on Mathematical Analysis 26 Journal of Functional Analysis 26 Discrete and Continuous Dynamical Systems. Series B 25 Physica D 24 Communications in Partial Differential Equations 23 Nonlinear Analysis. Real World Applications 20 Kinetic and Related Models 19 Mathematical Methods in the Applied Sciences 19 Nonlinearity 17 Computers & Mathematics with Applications 17 Calculus of Variations and Partial Differential Equations 16 Transactions of the American Mathematical Society 14 Mathematische Annalen 14 Journal of Nonlinear Science 12 Journal of Mathematical Physics 12 Applied Mathematics and Computation 12 Journal of Computational and Applied Mathematics 11 Acta Applicandae Mathematicae 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 NoDEA. Nonlinear Differential Equations and Applications 10 Journal of Mathematical Biology 10 Applied Mathematics Letters 10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 9 Journal of Evolution Equations 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Bulletin of Mathematical Biology 8 Communications on Pure and Applied Analysis 7 Advances in Mathematics 7 Duke Mathematical Journal 7 Mathematical and Computer Modelling 7 Journal of Scientific Computing 7 Annales Henri Poincaré 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Discrete and Continuous Dynamical Systems. Series S 7 Journal of Theoretical Biology 7 Séminaire Laurent Schwartz. EDP et Applications 6 Communications on Pure and Applied Mathematics 6 Journal of Computational Physics 6 Inventiones Mathematicae 6 Memoirs of the American Mathematical Society 6 Proceedings of the American Mathematical Society 6 European Journal of Applied Mathematics 6 SIAM Journal on Applied Dynamical Systems 6 Multiscale Modeling & Simulation 6 Science China. Mathematics 6 Annals of PDE 5 Applicable Analysis 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Quarterly of Applied Mathematics 5 Journal of Dynamics and Differential Equations 5 Journal of Mathematical Sciences (New York) 5 Communications in Contemporary Mathematics 5 Analysis & PDE 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Journal für die Reine und Angewandte Mathematik 4 Numerische Mathematik 4 SIAM Journal on Applied Mathematics 4 Abstract and Applied Analysis 4 Journal of the European Mathematical Society (JEMS) 4 Advanced Nonlinear Studies 4 Analysis and Applications (Singapore) 4 Boundary Value Problems 4 Networks and Heterogeneous Media 4 Nonlinear Analysis. Theory, Methods & Applications 3 Mathematical Biosciences 3 Mathematische Nachrichten 3 Advances in Applied Mathematics 3 The Journal of Geometric Analysis 3 Applied Mathematical Modelling 3 Applied Mathematics. Series B (English Edition) 3 Journal of Mathematical Fluid Mechanics 3 Communications in Nonlinear Science and Numerical Simulation 3 Differential Equations 3 Milan Journal of Mathematics 3 Mathematical Modelling of Natural Phenomena 2 Computers and Fluids 2 Journal d’Analyse Mathématique 2 Journal of Engineering Mathematics 2 Reports on Mathematical Physics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Archiv der Mathematik 2 Publications Mathématiques 2 Journal of the Mathematical Society of Japan 2 Mathematische Zeitschrift 2 Osaka Journal of Mathematics 2 Tohoku Mathematical Journal. Second Series 2 Chinese Annals of Mathematics. Series B 2 Applied Numerical Mathematics 2 Revista Matemática Iberoamericana 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni ...and 114 more Serials all top 5 Cited in 39 Fields 1,162 Partial differential equations (35-XX) 560 Biology and other natural sciences (92-XX) 197 Statistical mechanics, structure of matter (82-XX) 107 Fluid mechanics (76-XX) 95 Numerical analysis (65-XX) 65 Integral equations (45-XX) 44 Differential geometry (53-XX) 42 Probability theory and stochastic processes (60-XX) 30 Ordinary differential equations (34-XX) 29 Dynamical systems and ergodic theory (37-XX) 27 Classical thermodynamics, heat transfer (80-XX) 23 Mechanics of deformable solids (74-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 15 Operator theory (47-XX) 14 Relativity and gravitational theory (83-XX) 12 Optics, electromagnetic theory (78-XX) 10 Mechanics of particles and systems (70-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Global analysis, analysis on manifolds (58-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Quantum theory (81-XX) 6 Astronomy and astrophysics (85-XX) 4 Functional analysis (46-XX) 4 Computer science (68-XX) 4 Systems theory; control (93-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Functions of a complex variable (30-XX) 3 Statistics (62-XX) 3 Geophysics (86-XX) 3 Operations research, mathematical programming (90-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Convex and discrete geometry (52-XX) Citations by Year