Edit Profile (opens in new tab) Markowich, Peter Alexander Co-Author Distance Author ID: markowich.peter-alexander Published as: Markowich, Peter A.; Markowich, Peter; Markowich, P. A.; Markowich, P.; Markowich, Peter Alexander; Markovich, P. more...less External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 216 Publications since 1980, including 4 Books and 5 Additional arXiv Preprints 7 Contributions as Editor Biographic References: 1 Publication Co-Authors: 161 Co-Authors with 205 Joint Publications 5,775 Co-Co-Authors all top 5 Co-Authors 18 single-authored 24 Schmeiser, Christian 22 Sparber, Christof 17 Haskovec, Jan 13 Degond, Pierre 12 Jin, Shi 11 Arnold, Anton 11 Burger, Martin 11 Ringhofer, Christian A. 10 Bao, Weizhu 10 Perthame, Benoît 10 Wolfram, Marie-Therese 9 Gasser, Ingenuin 9 Hajaiej, Hichem 8 Dolbeault, Jean 8 Unterreiter, Andreas 7 Huang, Zhongyi 7 Mauser, Norbert Julius 7 Pietra, Paola 7 Toscani, Giuseppe 6 Caffarelli, Luis Ángel 6 Di Francesco, Marco 6 Jüngel, Ansgar 6 Pietschmann, Jan-Frederik 6 Poupaud, Frédéric 6 Renardy, Michael 6 Trabelsi, Saber 5 Carrillo de la Plata, José Antonio 5 Cordier, Stéphane 5 Wang, Shu 4 Brezzi, Franco 4 Kreusser, Lisa Maria 4 Li, Hailiang 4 Lorz, Alexander 4 Paul, Thierry 4 Sierra, Jesús 4 Zubelli, Jorge P. 3 Antonelli, Paolo 3 Astuto, Clarissa 3 Ben Abdallah, Naoufel 3 Engl, Heinz W. 3 Fellner, Klemens 3 Klein, Christian 3 Lederman, Claudia B. 3 Leitão, Antonio 3 Pohl, Carsten 3 Portaro, Simone 3 Russo, Giovanni 3 Weishäupl, Rada-Maria 2 Alhomedan, Suad 2 Aoki, Kazuo 2 Ascher, Uri M. 2 Athanassoulis, Agisillaos 2 Bardos, Claude Williams 2 Biler, Piotr 2 Boffi, Daniele 2 Brinkman, Daniel 2 Carles, Rémi 2 Chalub, Fabio A. C. C. 2 Chen, Huyuan 2 Cho, Yonggeun 2 Düring, Bertram 2 Fall, Mouhamed Moustapha 2 Golse, François 2 Jaksch, Dieter 2 Matevosyan, Norayr 2 Mei, Ming 2 Mielke, Alexander 2 Ölz, Dietmar 2 Pareschi, Lorenzo 2 Pilli, Giulia 2 Schönlieb, Carola-Bibiane 2 Steinrück, Herbert 2 Villani, Cédric 2 Weiss, Richard 2 Zheng, Chunxiong 1 Abdelhedi, Wael 1 Aki, Gonca L. 1 Albi, Giacomo 1 Alhemedan, Suad 1 Amadori, Debora 1 Andreianov, Boris 1 Artina, Marco 1 Bod’ová, Katarína 1 Bonilla, Luis Lopez 1 Borgna, Juan Pablo 1 Cai, Yongyong 1 Chai, Lihui 1 Chertock, Alina E. 1 Chtioui, Hichem 1 Chu, Shun-Yin 1 Ciepliński, Krzysztof 1 Danaila, Ionut 1 de Hoop, Maarten V. 1 Desvillettes, Laurent 1 Dolak-Struss, Yasmin 1 Duan, Renjun 1 Esteban, Maria J. 1 Fagioli, Simone 1 Fang, Di 1 Figalli, Alessio ...and 62 more Co-Authors all top 5 Serials 13 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 9 SIAM Journal on Mathematical Analysis 8 Communications in Mathematical Sciences 6 Archive for Rational Mechanics and Analysis 6 Journal of Computational Physics 6 Monatshefte für Mathematik 5 Journal of Mathematical Physics 5 Journal of Differential Equations 5 Applied Mathematics Letters 5 Communications in Partial Differential Equations 4 Nonlinearity 4 Transport Theory and Statistical Physics 4 SIAM Journal on Numerical Analysis 4 SIAM Journal on Applied Mathematics 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 4 Kinetic and Related Models 3 IMA Journal of Applied Mathematics 3 Journal of Statistical Physics 3 Mathematical Methods in the Applied Sciences 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 RAIRO. Modélisation Mathématique et Analyse Numérique 3 Asymptotic Analysis 3 Discrete and Continuous Dynamical Systems 3 Milan Journal of Mathematics 3 Multiscale Modeling & Simulation 2 Communications on Pure and Applied Mathematics 2 Inverse Problems 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Mathematics of Computation 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Numerische Mathematik 2 Mathematical and Computer Modelling 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Bollettino della Unione Matemàtica Italiana. Serie VII. B 2 Journal of Nonlinear Science 2 SIAM Journal on Scientific Computing 2 Electronic Journal of Differential Equations (EJDE) 2 Discrete and Continuous Dynamical Systems. Series B 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Analysis and Applications (Singapore) 2 Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Wave Motion 1 Calcolo 1 Journal of Functional Analysis 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 Quarterly of Applied Mathematics 1 SIAM Journal on Control and Optimization 1 Physica D 1 Revista Matemática Iberoamericana 1 COMPEL 1 Forum Mathematicum 1 Science in China. Series A 1 European Journal of Applied Mathematics 1 Journal of Non-Newtonian Fluid Mechanics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Dynamics and Differential Equations 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Journal of Mathematical Sciences (New York) 1 Matemática Contemporânea 1 Taiwanese Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 1 Acta Numerica 1 Complex Variables and Elliptic Equations 1 Pitman Research Notes in Mathematics Series 1 Series in Applied Mathematics (Paris) 1 Communications in Computational Physics 1 Journal of Dynamics and Games 1 Mathematics and Mechanics of Complex Systems 1 Nonlinear Analysis. Theory, Methods & Applications 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 SMAI Journal of Computational Mathematics all top 5 Fields 157 Partial differential equations (35-XX) 57 Statistical mechanics, structure of matter (82-XX) 53 Numerical analysis (65-XX) 42 Quantum theory (81-XX) 35 Fluid mechanics (76-XX) 27 Biology and other natural sciences (92-XX) 23 Optics, electromagnetic theory (78-XX) 21 Ordinary differential equations (34-XX) 13 Integral equations (45-XX) 9 Mechanics of deformable solids (74-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 General and overarching topics; collections (00-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Functional analysis (46-XX) 3 Operator theory (47-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Probability theory and stochastic processes (60-XX) 2 Real functions (26-XX) 2 Geophysics (86-XX) 2 Operations research, mathematical programming (90-XX) 2 Information and communication theory, circuits (94-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 190 Publications have been cited 5,086 times in 3,168 Documents Cited by ▼ Year ▼ Semiconductor equations. Zbl 0765.35001 Markowich, Peter A.; Ringhofer, Christian A.; Schmeiser, Christian 567 1990 Global solutions to the coupled chemotaxis-fluid equations. Zbl 1275.35005 Duan, Renjun; Lorz, Alexander; Markowich, Peter 255 2010 Homogenization limits and Wigner transforms. Zbl 0881.35099 Gérard, Patrick; Markowich, Peter A.; Mauser, Norbert J.; Poupaud, Frédéric 213 1997 On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime. Zbl 1006.65112 Bao, Weizhu; Jin, Shi; Markowich, Peter A. 192 2002 On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Zbl 0982.35113 Arnold, Anton; Markowich, Peter; Toscani, Giuseppe; Unterreiter, Andreas 190 2001 Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior. Zbl 1276.35103 Di Francesco, Marco; Lorz, Alexander; Markowich, Peter A. 159 2010 Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation. Zbl 1028.82501 Bao, Weizhu; Jaksch, Dieter; Markowich, Peter A. 157 2003 Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities. Zbl 0984.35027 Carrillo, J. A.; Jüngel, A.; Markowich, P. A.; Toscani, G.; Unterreiter, A. 152 2001 Kinetic models for chemotaxis and their drift-diffusion limits. Zbl 1052.92005 Chalub, Fabio A. C. C.; Markowich, Peter A.; Perthame, Benoît; Schmeiser, Christian 134 2004 On a one-dimensional steady-state hydrodynamic model for semiconductors. Zbl 0736.35129 Degond, P.; Markowich, P. A. 112 1990 Numerical study of time-splitting spectral discretizations of nonlinear Schrödinger equations in the semiclassical regimes. Zbl 1038.65099 Bao, Weizhu; Jin, Shi; Markowich, Peter A. 103 2003 Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach. Zbl 1250.76191 Chertock, A.; Fellner, K.; Kurganov, A.; Lorz, A.; Markowich, P. A. 79 2012 Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model. Zbl 1339.35246 Markowich, Peter A.; Titi, Edriss S.; Trabelsi, Saber 78 2016 Mathematical and computational methods for semiclassical Schrödinger equations. Zbl 1233.65071 Jin, Shi; Markowich, Peter; Sparber, Christof 74 2011 Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Zbl 1195.91127 Düring, Bertram; Markowich, Peter; Pietschmann, Jan-Frederik; Wolfram, Marie-Therese 73 2009 Ground, symmetric and central vortex states in rotating Bose-Einstein condensates. Zbl 1073.82004 Bao, Weizhu; Wang, Hanquan; Markowich, Peter A. 65 2005 A steady state potential flow model for semiconductors. Zbl 0808.35150 Degond, Pierre; Markowich, Peter A. 64 1993 Quantum hydrodynamics, Wigner transforms and the classical limit. Zbl 0877.76087 Gasser, Ingenuin; Markowich, Peter A. 62 1997 The classical limit of a self-consistent quantum-Vlasov equation in 3D. Zbl 0772.35061 Markowich, Peter A.; Mauser, Norbert J. 61 1993 On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis. Zbl 1139.82326 Markowich, P. A.; Villani, C. 60 2000 The three-dimensional Wigner-Poisson problem: Existence, uniqueness and approximation. Zbl 0739.35080 Brezzi, Franco; Markowich, Peter A. 60 1991 Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit. Zbl 0928.65109 Markowich, Peter A.; Pietra, Paola; Pohl, Carsten 57 1999 Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors. Zbl 1119.35310 Li, Hailiang; Markowich, Peter; Mei, Ming 56 2002 On the Gross-Pitaevskii equation for trapped dipolar quantum gases. Zbl 1157.35102 Carles, Rémi; Markowich, Peter A.; Sparber, Christof 54 2008 The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors. Zbl 1045.35088 Hsiao, Ling; Markowich, Peter A.; Wang, Shu 53 2003 A time-splitting spectral scheme for the Maxwell-Dirac system. Zbl 1070.81040 Huang, Zhongyi; Jin, Shi; Markowich, Peter A.; Sparber, Christof; Zheng, Chunxiong 51 2005 Model hierarchies for cell aggregation by chemotaxis. Zbl 1094.92009 Chalub, Fabio; Dolak-Struss, Yasmin; Markowich, Peter; Oelz, Dietmar; Schmeiser, Christian; Soreff, Alexander 50 2006 Numerical study of fractional nonlinear Schrödinger equations. Zbl 1372.65284 Klein, Christian; Sparber, Christof; Markowich, Peter 46 2014 Mean field games with nonlinear mobilities in pedestrian dynamics. Zbl 1304.49008 Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie-Therese 46 2014 On the Hughes’ model for pedestrian flow: the one-dimensional case. Zbl 1229.35139 Di Francesco, Marco; Markowich, Peter A.; Pietschmann, Jan-Frederik; Wolfram, Marie-Therese 43 2011 A Wigner-function approach to (semi)classical limits: Electrons in a periodic potential. Zbl 0805.35106 Markowich, P. A.; Mauser, N. J.; Poupaud, F. 43 1994 On the equivalence of the Schrödinger and the quantum Liouville equations. Zbl 0696.47042 Markowich, Peter A. 42 1989 A phase plane analysis of transonic solutions for the hydrodynamic semiconductor model. Zbl 0800.76032 Ascher, Uri M.; Markowich, Peter A.; Pietra, Paola; Schmeiser, Christian 41 1991 On a one-dimensional Schrödinger-Poisson scattering model. Zbl 0885.34067 Ben Abdallah, Naoufel; Degond, Pierre; Markowich, Peter A. 39 1997 Numerical simulation of a generalized Zakharov system. Zbl 1079.65101 Jin, Shi; Markowich, Peter A.; Zheng, Chunxiong 38 2004 On generalized Csiszár-Kullback inequalities. Zbl 1015.94003 Unterreiter, Andreas; Arnold, Anton; Markowich, Peter; Toscani, Giuseppe 35 2000 The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model. Zbl 1018.82024 Gasser, Ingenuin; Levermore, C. David; Markowich, Peter A.; Schmeiser, Christian 33 2001 Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109 Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C. 33 2004 Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation. Zbl 1128.37043 Klein, Christian; Sparber, Christof; Markowich, Peter 33 2007 On steady state Euler-Poisson models for semiconductors. Zbl 0755.35138 Markowich, Peter A. 31 1991 Wigner functions versus WKB-methods in multivalued geometrical optics. Zbl 1069.81552 Sparber, Christof; Markowich, Peter A.; Mauser, Norbert J. 29 2003 An analysis of quantum Fokker-Planck models: a Wigner function approach. Zbl 1062.35097 Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan 29 2004 On large time asymptotics for drift-diffusion-Poisson systems. Zbl 1017.82041 Arnold, Anton; Markowich, Peter; Toscani, Giuseppe 28 2000 On uniform decay of the entropy for reaction-diffusion systems. Zbl 1338.35245 Mielke, Alexander; Haskovec, Jan; Markowich, Peter A. 28 2015 Mathematical analysis of a PDE system for biological network formation. Zbl 1345.35120 Haskovec, Jan; Markowich, Peter; Perthame, Benoit 26 2015 A Wigner-measure analysis of the Dufort–Frankel scheme for the Schrödinger equation. Zbl 1029.65098 Markowich, Peter A.; Pietra, Paola; Pohl, Carsten; Stimming, Hans Peter 25 2002 Closure conditions for classical and quantum moment hierarchies in the small-temperature limit. Zbl 0871.76078 Gasser, Ingenuin; Markowich, Peter A.; Ringhofer, Christian A. 23 1996 Nonlinear diffusion as limit of kinetic equations with relaxation collision kernels. Zbl 1148.76047 Dolbeault, Jean; Markowich, Peter; Oelz, Dietmar; Schmeiser, Christian 23 2007 Notes on a PDE system for biological network formation. Zbl 1334.35101 Haskovec, Jan; Markowich, Peter; Perthame, Benoît; Schlottbom, Matthias 23 2016 An analysis of the quantum Liouville equation. Zbl 0682.46047 Markowich, P. A.; Ringhofer, C. A. 22 1989 A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene. Zbl 1349.65271 Brinkman, D.; Heitzinger, C.; Markowich, P. A. 22 2014 Quasi-neutral limit of a nonlinear drift diffusion model for semiconductors. Zbl 1016.82034 Gasser, Ingenuin; Hsiao, Ling; Markowich, Peter A.; Wang, Shu 21 2002 Quasi-neutral limit of the drift diffusion models for semiconductors: the case of general sign-changing doping profile. Zbl 1103.76070 Wang, Shu; Xin, Zhouping; Markowich, Peter A. 21 2006 Biological transportation networks: modeling and simulation. Zbl 1329.35313 Albi, Giacomo; Artina, Marco; Foransier, Massimo; Markowich, Peter A. 21 2016 Optimal bilinear control of Gross-Pitaevskii equations. Zbl 1277.49005 Hintermüller, Michael; Marahrens, Daniel; Markowich, Peter A.; Sparber, Christof 21 2013 Semiclassical asymptotics for the Maxwell-Dirac system. Zbl 1062.81059 Sparber, C.; Markowich, P. 20 2003 Semiclassical, \(t\to \infty\) asymptotics and dispersive effects for Hartree-Fock systems. Zbl 0924.35125 Gasser, I.; Illner, R.; Markowich, P. A.; Schmeiser, C. 19 1998 Continuous limit of a crowd motion and herding model: analysis and numerical simulations. Zbl 1347.35128 Burger, Martin; Markowich, Peter Alexander; Pietschmann, Jan-Frederik 19 2011 On a Boltzmann-type price formation model. Zbl 1372.91039 Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 19 2013 A review of dispersive limits of (non)linear Schrödinger-type equations. Zbl 0972.35112 Gasser, Ingenuin; Lin, Chi-Kun; Markowich, Peter A. 18 2000 Uniform asymptotic representation of solutions of the basic semiconductor-device equations. Zbl 0614.34013 Markowich, Peter A.; Schmeiser, Christian 18 1986 Poincaré inequalities for linearizations of very fast diffusion equations. Zbl 1011.35025 Carrillo, J. A.; Lederman, C.; Markowich, P. A.; Toscani, G. 18 2002 A singularly perturbed boundary value problem modelling a semiconductor device. Zbl 0559.34058 Markowich, Peter A.; Ringhofer, Christian A. 17 1984 A system of convection-diffusion equations with small diffusion coefficient arising in semiconductor physics. Zbl 0709.35058 Markowich, Peter A.; Szmolyan, Peter 17 1989 A Bloch decomposition – based split-step pseudospectral method for quantum dynamics with periodic potentials. Zbl 1136.65093 Huang, Zhongyi; Jin, Shi; Markowich, Peter A.; Sparber, Christof 16 2007 Thermal equilibrium states of the quantum hydrodynamic model for semiconductors in one dimension. Zbl 0829.35127 Brezzi, F.; Gasser, I.; Markowich, P. A.; Schmeiser, C. 16 1995 Decay to equilibrium for energy-reaction-diffusion systems. Zbl 1387.35352 Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander 16 2018 On singular limits of mean-field equations. Zbl 1054.76086 Dolbeault, Jean; Markowich, Peter A.; Unterreiter, Andreas 16 2001 Existence and nonlinear stability of stationary states of the Schrödinger-Poisson system. Zbl 1001.82107 Markowich, Peter A.; Rein, Gerhard; Wolansky, Gershon 16 2002 Semiclassical asymptotics for weakly nonlinear Bloch waves. Zbl 1104.81049 Carles, Rémi; Markowich, Peter A.; Sparber, Christof 16 2004 On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass. Zbl 1024.35040 Lederman, Claudia; Markowich, Peter A. 16 2003 On the XFEL Schrödinger equation: highly oscillatory magnetic potentials and time averaging. Zbl 1294.35129 Antonelli, Paolo; Athanassoulis, Agisillaos; Hajaiej, Hichem; Markowich, Peter 16 2014 On a price formation free boundary model by Lasry and Lions. Zbl 1216.91012 Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F. 15 2011 On a parabolic free boundary equation modeling price formation. Zbl 1183.35278 Markowich, P. A.; Matevosyan, N.; Pietschmann, J.-F.; Wolfram, M.-T. 15 2009 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004 15 2014 A theory for the approximation of solutions of boundary value problems on infinite intervals. Zbl 0498.34007 Markowich, Peter A. 14 1982 The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems. Zbl 1186.35101 Di Francesco, Marco; Fellner, Klemens; Markowich, Peter A. 14 2008 Fast conservative and entropic numerical methods for the boson Boltzmann equation. Zbl 1204.82031 Markowich, Peter A.; Pareschi, Lorenzo 14 2005 Asymptotic behavior of subsonic entropy solutions of the isentropic Euler-Poisson equations. Zbl 1031.35100 Li, Hailiang; Markowich, Peter; Mei, Ming 14 2002 ODE- and PDE-based modeling of biological transportation networks. Zbl 1433.35421 Haskovec, Jan; Kreusser, Lisa Maria; Markowich, Peter 14 2019 Analysis of boundary value problems on infinite intervals. Zbl 0528.34017 Markowich, Peter A. 13 1983 A singular perturbation analysis of the fundamental semiconductor device equations. Zbl 0568.35007 Markowich, Peter A. 13 1984 Travelling wave analysis of an isothermal Euler-Poisson model. Zbl 0884.35126 Cordier, S.; Degond, P.; Markowich, P.; Schmeiser, C. 13 1996 A drift-diffusion-reaction model for excitonic photovoltaic bilayers: asymptotic analysis and a 2D HDG finite element scheme. Zbl 1264.35118 Brinkman, Daniel; Fellner, Klemens; Markowich, Peter A.; Wolfram, Marie-Therese 13 2013 Rigorous continuum limit for the discrete network formation problem. Zbl 1428.35652 Haskovec, Jan; Kreusser, Lisa Maria; Markowich, Peter 13 2019 A nonlinear Volterra integrodifferential equation describing the stretching of polymeric liquids. Zbl 0507.45013 Markowich, Peter A.; Renardy, M. 12 1983 Identification of doping profiles in semiconductor devices. Zbl 0989.35139 Burger, Martin; Engl, Heinz W.; Markowich, Peter A.; Pietra, Paola 12 2001 Numerical simulation of the nonlinear Schrödinger equation with multidimensional periodic potentials. Zbl 1173.65341 Huang, Zhongyi; Jin, Shi; Markowich, Peter A.; Sparber, Christof 12 2008 Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. I: Homogeneous problems. Zbl 1079.81026 Gosse, Laurent; Markowich, Peter A. 12 2004 On the long-time behavior of the quantum Fokker-Planck equation. Zbl 1061.35095 Sparber, C.; Carrillo, J. A.; Dolbeault, J.; Markowich, P. A. 12 2004 Global existence and asymptotic behavior for a semiconductor drift-diffusion-Poisson model. Zbl 1157.35013 Hao, Wu; Markowich, Peter A.; Zheng, Songmu 12 2008 High field approximations of the spherical harmonics expansion model for semiconductors. Zbl 1174.82345 Ben Abdallah, N.; Degond, P.; Markowich, P.; Schmeiser, C. 11 2001 Scattering of solitons of the Klein-Gordon equation coupled to a classical particle. Zbl 1061.35070 Imaikin, Valery; Komech, Alexander; Markowich, Peter A. 11 2003 Macroscopic theory of charged quantum fluids. Zbl 0882.76107 Gasser, I.; Markowich, P. A.; Schmidt, D.; Unterreiter, A. 11 1995 An asymptotic analysis of one-dimensional models of semiconductur devices. Zbl 0639.34016 Markowich, P. A.; Ringhofer, C. A.; Schmeiser, C. 10 1986 The drift-diffusion limit for electron-phonon interaction in semiconductors. Zbl 0884.45006 Markowich, Peter A.; Schmeiser, Christian 10 1997 A mesoscopic model of biological transportation networks. Zbl 1433.35416 Burger, Martin; Haskovec, Jan; Markowich, Peter; Ranetbauer, Helene 10 2019 Bohmian measures and their classical limit. Zbl 1195.81060 Markowich, Peter; Paul, Thierry; Sparber, Christof 10 2010 On Maxwellian equilibria of insulated semiconductors. Zbl 0961.35158 Caffarelli, Luis; Dolbeault, Jean; Markowich, Peter A.; Schmeiser, Christian 9 2000 Classical limit for semirelativistic Hartree systems. Zbl 1152.81307 Aki, Gonca L.; Markowich, Peter A.; Sparber, Christof 9 2008 Emergence of biological transportation networks as a self-regulated process. Zbl 1518.35216 Haskovec, Jan; Markowich, Peter; Portaro, Simone 1 2023 Tensor PDE model of biological network formation. Zbl 1492.35365 Haskovec, Jan; Markowich, Peter; Pilli, Giulia 1 2022 Selection dynamics for deep neural networks. Zbl 1448.49029 Liu, Hailiang; Markowich, Peter 3 2020 ODE- and PDE-based modeling of biological transportation networks. Zbl 1433.35421 Haskovec, Jan; Kreusser, Lisa Maria; Markowich, Peter 14 2019 Rigorous continuum limit for the discrete network formation problem. Zbl 1428.35652 Haskovec, Jan; Kreusser, Lisa Maria; Markowich, Peter 13 2019 A mesoscopic model of biological transportation networks. Zbl 1433.35416 Burger, Martin; Haskovec, Jan; Markowich, Peter; Ranetbauer, Helene 10 2019 Implicit and semi-implicit numerical schemes for the gradient flow of the formation of biological transport networks. Zbl 1437.65095 Fang, Di; Jin, Shi; Markowich, Peter; Perthame, Benoît 6 2019 Auxin transport model for leaf venation. Zbl 1472.92147 Haskovec, Jan; Jönsson, Henrik; Kreusser, Lisa Maria; Markowich, Peter 5 2019 Non-uniqueness of weak solutions of the quantum-hydrodynamic system. Zbl 1421.35004 Markowich, Peter; Sierra, Jesús 4 2019 Murray’s law for discrete and continuum models of biological networks. Zbl 1428.92029 Haskovec, Jan; Markowich, Peter; Pilli, Giulia 3 2019 Decay to equilibrium for energy-reaction-diffusion systems. Zbl 1387.35352 Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter; Mielke, Alexander 16 2018 Pattern formation of a nonlocal, anisotropic interaction model. Zbl 1383.35024 Burger, Martin; Düring, Bertram; Kreusser, Lisa Maria; Markowich, Peter A.; Schönlieb, Carola-Bibiane 7 2018 Fundamental solutions for Schrödinger operators with general inverse square potentials. Zbl 1395.35002 Chen, Huyuan; Alhomedan, Suad; Hajaiej, Hichem; Markowich, Peter 5 2018 Well posedness and maximum entropy approximation for the dynamics of quantitative traits. Zbl 1398.35245 Boďová, Katarína; Haskovec, Jan; Markowich, Peter 1 2018 Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity. Zbl 1375.35480 Cho, Yonggeun; Fall, Mouhamed M.; Hajaiej, Hichem; Markowich, Peter A.; Trabelsi, Saber 6 2017 Complete study of the existence and uniqueness of solutions for semilinear elliptic equations involving measures concentrated on boundary. Zbl 1387.35603 Chen, Huyuan; Alhomedan, Suad; Hajaiej, Hichem; Markowich, Peter 4 2017 Existence of solutions to perturbed fractional Nirenberg problems. Zbl 1359.35210 Abdelhedi, Wael; Alhemedan, Suad; Chtioui, Hichem; Hajaiej, Hichem; Markowich, Peter A. 1 2017 Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model. Zbl 1339.35246 Markowich, Peter A.; Titi, Edriss S.; Trabelsi, Saber 78 2016 Notes on a PDE system for biological network formation. Zbl 1334.35101 Haskovec, Jan; Markowich, Peter; Perthame, Benoît; Schlottbom, Matthias 23 2016 Biological transportation networks: modeling and simulation. Zbl 1329.35313 Albi, Giacomo; Artina, Marco; Foransier, Massimo; Markowich, Peter A. 21 2016 Parabolic free boundary price formation models under market size fluctuations. Zbl 1355.35184 Markowich, Peter; Teichmann, Josef; Wolfram, Marie-Therese 5 2016 On uniform decay of the entropy for reaction-diffusion systems. Zbl 1338.35245 Mielke, Alexander; Haskovec, Jan; Markowich, Peter A. 28 2015 Mathematical analysis of a PDE system for biological network formation. Zbl 1345.35120 Haskovec, Jan; Markowich, Peter; Perthame, Benoit 26 2015 On the Gross-Pitaevskii equation with pumping and decay: stationary states and their stability. Zbl 1318.35109 Sierra, Jesús; Kasimov, Aslan; Markowich, Peter; Weishäupl, Rada-Maria 4 2015 Hamiltonian evolution of monokinetic measures with rough momentum profile. Zbl 1329.35259 Bardos, Claude; Golse, François; Markowich, Peter; Paul, Thierry 3 2015 Stationary solutions of Keller-Segel-type crowd motion and herding models: multiplicity and dynamical stability. Zbl 1336.35337 Dolbeault, Jean; Jankowiak, Gaspard; Markowich, Peter 2 2015 On the classical limit of the Schrödinger equation. Zbl 1332.35312 Bardos, Claude; Golse, François; Markowich, Peter; Paul, Thierry 2 2015 Numerical study of fractional nonlinear Schrödinger equations. Zbl 1372.65284 Klein, Christian; Sparber, Christof; Markowich, Peter 46 2014 Mean field games with nonlinear mobilities in pedestrian dynamics. Zbl 1304.49008 Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie-Therese 46 2014 A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene. Zbl 1349.65271 Brinkman, D.; Heitzinger, C.; Markowich, P. A. 22 2014 On the XFEL Schrödinger equation: highly oscillatory magnetic potentials and time averaging. Zbl 1294.35129 Antonelli, Paolo; Athanassoulis, Agisillaos; Hajaiej, Hichem; Markowich, Peter 16 2014 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004 15 2014 On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302 Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 9 2014 Numerical simulations of X-ray free electron lasers (XFEL). Zbl 1319.78015 Antonelli, Paolo; Athanassoulis, Agissilaos; Huang, Zhongyi; Markowich, Peter A. 9 2014 WKB analysis of Bohmian dynamics. Zbl 1341.35139 Figalli, A.; Klein, C.; Markowich, P.; Sparber, C. 6 2014 Variational approach to the orbital stability of standing waves of the Gross-Pitaevskii equation. Zbl 1304.35655 Selem, Fouad Hadj; Hajaiej, Hichem; Markowich, Peter A.; Trabelsi, Saber 5 2014 Multiconfiguration Hartree-Fock theory for pseudorelativistic systems: the time-dependent case. Zbl 1291.35256 Hajaiej, Hichem; Markowich, Peter A.; Trabelsi, Saber 5 2014 Minimizers of a class of constrained vectorial variational problems. I. Zbl 1307.49012 Hajaiej, Hichem; Markowich, Peter A.; Trabelsi, Saber 4 2014 Optimal bilinear control of Gross-Pitaevskii equations. Zbl 1277.49005 Hintermüller, Michael; Marahrens, Daniel; Markowich, Peter A.; Sparber, Christof 21 2013 On a Boltzmann-type price formation model. Zbl 1372.91039 Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 19 2013 A drift-diffusion-reaction model for excitonic photovoltaic bilayers: asymptotic analysis and a 2D HDG finite element scheme. Zbl 1264.35118 Brinkman, Daniel; Fellner, Klemens; Markowich, Peter A.; Wolfram, Marie-Therese 13 2013 Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach. Zbl 1250.76191 Chertock, A.; Fellner, K.; Kurganov, A.; Lorz, A.; Markowich, P. A. 79 2012 On the dynamics of Bohmian measures. Zbl 1256.35171 Markowich, Peter; Paul, Thierry; Sparber, Christof 6 2012 Mathematical and computational methods for semiclassical Schrödinger equations. Zbl 1233.65071 Jin, Shi; Markowich, Peter; Sparber, Christof 74 2011 On the Hughes’ model for pedestrian flow: the one-dimensional case. Zbl 1229.35139 Di Francesco, Marco; Markowich, Peter A.; Pietschmann, Jan-Frederik; Wolfram, Marie-Therese 43 2011 Continuous limit of a crowd motion and herding model: analysis and numerical simulations. Zbl 1347.35128 Burger, Martin; Markowich, Peter Alexander; Pietschmann, Jan-Frederik 19 2011 On a price formation free boundary model by Lasry and Lions. Zbl 1216.91012 Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F. 15 2011 On a price formation free boundary model by Lasry and Lions: the Neumann problem. Zbl 1233.91336 Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie-Therese 8 2011 Global solutions to the coupled chemotaxis-fluid equations. Zbl 1275.35005 Duan, Renjun; Lorz, Alexander; Markowich, Peter 255 2010 Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior. Zbl 1276.35103 Di Francesco, Marco; Lorz, Alexander; Markowich, Peter A. 159 2010 Bohmian measures and their classical limit. Zbl 1195.81060 Markowich, Peter; Paul, Thierry; Sparber, Christof 10 2010 Numerical simulation of trapped dipolar quantum gases: collapse studies and vortex dynamics. Zbl 1188.81064 Huang, Zhongyi; Markowich, Peter A.; Sparber, Christof 3 2010 Decomposition-based method for high frequency waves in periodic media. Zbl 1227.35022 Huang, Zhongyi; Jin, Shi; Markowich, Peter A.; Sparber, Christof 1 2010 Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Zbl 1195.91127 Düring, Bertram; Markowich, Peter; Pietschmann, Jan-Frederik; Wolfram, Marie-Therese 73 2009 On a parabolic free boundary equation modeling price formation. Zbl 1183.35278 Markowich, P. A.; Matevosyan, N.; Pietschmann, J.-F.; Wolfram, M.-T. 15 2009 On the Bloch decomposition based spectral method for wave propagation in periodic media. Zbl 1231.78019 Huang, Zhongyi; Jin, Shi; Markowich, Peter A.; Sparber, Christof 3 2009 On the Gross-Pitaevskii equation for trapped dipolar quantum gases. Zbl 1157.35102 Carles, Rémi; Markowich, Peter A.; Sparber, Christof 54 2008 The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems. Zbl 1186.35101 Di Francesco, Marco; Fellner, Klemens; Markowich, Peter A. 14 2008 Numerical simulation of the nonlinear Schrödinger equation with multidimensional periodic potentials. Zbl 1173.65341 Huang, Zhongyi; Jin, Shi; Markowich, Peter A.; Sparber, Christof 12 2008 Global existence and asymptotic behavior for a semiconductor drift-diffusion-Poisson model. Zbl 1157.35013 Hao, Wu; Markowich, Peter A.; Zheng, Songmu 12 2008 Classical limit for semirelativistic Hartree systems. Zbl 1152.81307 Aki, Gonca L.; Markowich, Peter A.; Sparber, Christof 9 2008 The Willmore functional and instabilities in the Cahn-Hilliard equation. Zbl 1154.35009 Burger, Martin; Chu, Shun-Yin; Markowich, Peter A.; Schönlieb, Carola-Bibiane 3 2008 Mathematical methods and modeling of biophysical phenomena. Zbl 1155.92302 Perthame, Benoit; Markowich, Peter; Zubelli, Jorge P. 2 2008 Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation. Zbl 1128.37043 Klein, Christian; Sparber, Christof; Markowich, Peter 33 2007 Nonlinear diffusion as limit of kinetic equations with relaxation collision kernels. Zbl 1148.76047 Dolbeault, Jean; Markowich, Peter; Oelz, Dietmar; Schmeiser, Christian 23 2007 A Bloch decomposition – based split-step pseudospectral method for quantum dynamics with periodic potentials. Zbl 1136.65093 Huang, Zhongyi; Jin, Shi; Markowich, Peter A.; Sparber, Christof 16 2007 Applied partial differential equations: a visual approach. Zbl 1109.35001 Markowich, Peter A. 5 2007 Convergence rate of dimension reduction in Bose-Einstein condensates. Zbl 1196.82065 Bao, Weizhu; Ge, Yunyi; Jaksch, Dieter; Markowich, Peter A.; Weishäupl, Rada M. 4 2007 Inverse problems for semiconductors: models and methods. Zbl 1115.82039 Leitão, A.; Markowich, P. A.; Zubelli, J. P. 3 2007 A Hermite pseudo-spectral method for solving systems of Gross-Pitaevskii equations. Zbl 1151.35087 Weishäuptl, Rada M.; Schmeiser, Christian; Markowich, Peter A.; Borgna, Juan Pablo 3 2007 Kinetic relaxation models for energy transport. Zbl 1126.82034 Aoki, Kazuo; Markowich, Peter; Takata, Shigeru 1 2007 Model hierarchies for cell aggregation by chemotaxis. Zbl 1094.92009 Chalub, Fabio; Dolak-Struss, Yasmin; Markowich, Peter; Oelz, Dietmar; Schmeiser, Christian; Soreff, Alexander 50 2006 Quasi-neutral limit of the drift diffusion models for semiconductors: the case of general sign-changing doping profile. Zbl 1103.76070 Wang, Shu; Xin, Zhouping; Markowich, Peter A. 21 2006 On inverse doping profile problems for the stationary voltage-current map. Zbl 1099.35173 Leitão, A.; Markowich, P. A.; Zubelli, J. P. 7 2006 Ground, symmetric and central vortex states in rotating Bose-Einstein condensates. Zbl 1073.82004 Bao, Weizhu; Wang, Hanquan; Markowich, Peter A. 65 2005 A time-splitting spectral scheme for the Maxwell-Dirac system. Zbl 1070.81040 Huang, Zhongyi; Jin, Shi; Markowich, Peter A.; Sparber, Christof; Zheng, Chunxiong 51 2005 Fast conservative and entropic numerical methods for the boson Boltzmann equation. Zbl 1204.82031 Markowich, Peter A.; Pareschi, Lorenzo 14 2005 On the Gross-Pitaevskii equation with strongly anisotropic confinement: formal asymptotics and numerical experiments. Zbl 1075.35073 Bao, Weizhu; Markowich, Peter A.; Schmeiser, Christian; Weishäupl, Rada M. 7 2005 Kinetic models for chemotaxis and their drift-diffusion limits. Zbl 1052.92005 Chalub, Fabio A. C. C.; Markowich, Peter A.; Perthame, Benoît; Schmeiser, Christian 134 2004 Numerical simulation of a generalized Zakharov system. Zbl 1079.65101 Jin, Shi; Markowich, Peter A.; Zheng, Chunxiong 38 2004 Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109 Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C. 33 2004 An analysis of quantum Fokker-Planck models: a Wigner function approach. Zbl 1062.35097 Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan 29 2004 Semiclassical asymptotics for weakly nonlinear Bloch waves. Zbl 1104.81049 Carles, Rémi; Markowich, Peter A.; Sparber, Christof 16 2004 Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice. I: Homogeneous problems. Zbl 1079.81026 Gosse, Laurent; Markowich, Peter A. 12 2004 On the long-time behavior of the quantum Fokker-Planck equation. Zbl 1061.35095 Sparber, C.; Carrillo, J. A.; Dolbeault, J.; Markowich, P. A. 12 2004 Steady states for Streater’s energy-transport models of self-gravitating particles. Zbl 1044.82013 Biler, Piotr; Dolbeault, Jean; Esteban, Maria J.; Markowich, Peter A.; Nadzieja, Tadeusz 8 2004 On inverse problems for semiconductor equations. Zbl 1214.82122 Burger, M.; Engl, H. W.; Leitao, A.; Markowich, P. A. 6 2004 Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation. Zbl 1106.82344 Bao, Weizhu; Pareschi, Lorenzo; Markowich, Peter A. 4 2004 Behavior of the free boundary near contact points with the fixed boundary for nonlinear elliptic equations. Zbl 1064.35215 Matevosyan, Norayr; Markowich, Peter A. 1 2004 Entropy dissipation and Wasserstein metric methods for the viscous Burgers’ equation: Convergence to diffusive waves. Zbl 1062.35111 Di Francesco, Marco; Markowich, Peter A. 1 2004 Erratum: “Semiclassical asymptotics for the Maxwell-Dirac system”. Zbl 1064.81508 Sparber, C.; Markowich, P. 1 2004 Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation. Zbl 1028.82501 Bao, Weizhu; Jaksch, Dieter; Markowich, Peter A. 157 2003 Numerical study of time-splitting spectral discretizations of nonlinear Schrödinger equations in the semiclassical regimes. Zbl 1038.65099 Bao, Weizhu; Jin, Shi; Markowich, Peter A. 103 2003 The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors. Zbl 1045.35088 Hsiao, Ling; Markowich, Peter A.; Wang, Shu 53 2003 Wigner functions versus WKB-methods in multivalued geometrical optics. Zbl 1069.81552 Sparber, Christof; Markowich, Peter A.; Mauser, Norbert J. 29 2003 Semiclassical asymptotics for the Maxwell-Dirac system. Zbl 1062.81059 Sparber, C.; Markowich, P. 20 2003 On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass. Zbl 1024.35040 Lederman, Claudia; Markowich, Peter A. 16 2003 Scattering of solitons of the Klein-Gordon equation coupled to a classical particle. Zbl 1061.35070 Imaikin, Valery; Komech, Alexander; Markowich, Peter A. 11 2003 Recent progress on quantum hydrodynamic models for semiconductors. Zbl 1134.82338 Jüngel, Ansgar; Li, Hailiang; Markowich, Peter A.; Wang, Shu 2 2003 On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime. Zbl 1006.65112 Bao, Weizhu; Jin, Shi; Markowich, Peter A. 192 2002 ...and 90 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,419 Authors 71 Markowich, Peter Alexander 48 Winkler, Michael 47 Bao, Weizhu 47 Carrillo de la Plata, José Antonio 42 Jüngel, Ansgar 41 Dolbeault, Jean 40 Wang, Shu 36 Jin, Shi 28 Toscani, Giuseppe 26 Bellomo, Nicola 26 Zhang, Kaijun 25 Degond, Pierre 25 Liu, Hailiang 24 Arnold, Anton 24 Mei, Ming 24 Sparber, Christof 23 Zheng, Jiashan 22 Li, Hailiang 22 Li, Yeping 22 Peng, Yuejun 22 Soler, Juan S. 22 Xiang, Zhaoyin 21 Cai, Yongyong 21 Perthame, Benoît 20 Carles, Rémi 20 Klein, Christian 20 Méhats, Florian 20 Wang, Tingchun 18 Bal, Guillaume 18 Ben Abdallah, Naoufel 18 Martínez Gamba, Irene 18 Guo, Boling 18 Schmeiser, Christian 17 Feng, Binhua 17 Ryzhik, Lenya 17 Wolfram, Marie-Therese 16 Kang, Kyungkeun 16 Klar, Axel 16 López, José Luis 16 Mauser, Norbert Julius 16 Paul, Thierry 16 Tan, Zhong 15 Burger, Martin 15 Chainais-Hillairet, Claire 15 Fermanian-Kammerer, Clotilde 15 Gosse, Laurent 15 Hsiao, Ling 15 Liu, Chun 15 Lu, Jianfeng 15 Marcati, Pierangelo 15 Pareschi, Lorenzo 15 Tang, Qinglin 14 Calvez, Vincent 14 Tang, Xianhua 14 Wang, Hanquan 14 Zhang, Guojing 14 Zhang, Qian 13 Chen, Li 13 Pinaud, Olivier 13 Tao, Youshan 13 Vauchelet, Nicolas 13 Wang, Yulan 13 Xu, Jiang 12 Antoine, Xavier 12 Antonelli, Paolo 12 Fellner, Klemens 12 Goudon, Thierry 12 Ha, Seung-Yeal 12 Mielke, Alexander 12 Mohan, Manil Thankamani 12 Romano, Vittorio 12 Titi, Edriss Saleh 12 Yang, Xu 12 Yu, Huimin 11 Chen, Sitong 11 Di Francesco, Marco 11 Feng, Yuehong 11 Haskovec, Jan 11 Li, Xianggui 11 Masmoudi, Nader 11 Nieto, Juanjo 11 Sacco, Riccardo 11 Su, Chunmei 11 Vazquez, Juan Luis 11 Yang, Jianwei 11 Zhou, Zhennan 11 Zweifel, Paul F. 10 Hajaiej, Hichem 10 Lange, Horst 10 Li, Bin 10 Li, Jiyong 10 Liu, Jianguo 10 Poupaud, Frédéric 10 Ringhofer, Christian A. 10 Tang, Bao Quoc 10 Thalhammer, Mechthild 10 Wang, Zhian 10 Yin, Jia 10 Zanella, Mattia 9 Albi, Giacomo ...and 3,319 more Authors all top 5 Cited in 354 Serials 189 Journal of Differential Equations 163 Journal of Computational Physics 146 M\(^3\)AS. 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Série VI 6 Journal of the European Mathematical Society (JEMS) 6 Acta Numerica ...and 254 more Serials all top 5 Cited in 50 Fields 2,433 Partial differential equations (35-XX) 806 Numerical analysis (65-XX) 772 Statistical mechanics, structure of matter (82-XX) 674 Fluid mechanics (76-XX) 537 Biology and other natural sciences (92-XX) 403 Quantum theory (81-XX) 206 Optics, electromagnetic theory (78-XX) 140 Probability theory and stochastic processes (60-XX) 128 Dynamical systems and ergodic theory (37-XX) 123 Calculus of variations and optimal control; optimization (49-XX) 109 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 102 Ordinary differential equations (34-XX) 89 Operator theory (47-XX) 76 Systems theory; control (93-XX) 70 Integral equations (45-XX) 54 Mechanics of deformable solids (74-XX) 47 Functional analysis (46-XX) 47 Operations research, mathematical programming (90-XX) 45 Real functions (26-XX) 39 Global analysis, analysis on manifolds (58-XX) 31 Classical thermodynamics, heat transfer (80-XX) 31 Information and communication theory, circuits (94-XX) 26 Mechanics of particles and systems (70-XX) 26 Astronomy and astrophysics (85-XX) 25 Harmonic analysis on Euclidean spaces (42-XX) 21 Computer science (68-XX) 20 Approximations and expansions (41-XX) 12 General and overarching topics; collections (00-XX) 12 Differential geometry (53-XX) 12 Relativity and gravitational theory (83-XX) 11 Difference and functional equations (39-XX) 11 Statistics (62-XX) 11 Geophysics (86-XX) 9 Special functions (33-XX) 5 Potential theory (31-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Topological groups, Lie groups (22-XX) 4 Measure and integration (28-XX) 3 Algebraic geometry (14-XX) 3 Abstract harmonic analysis (43-XX) 3 Integral transforms, operational calculus (44-XX) 2 History and biography (01-XX) 2 Group theory and generalizations (20-XX) 2 Functions of a complex variable (30-XX) 2 General topology (54-XX) 1 Number theory (11-XX) 1 Category theory; homological algebra (18-XX) 1 Sequences, series, summability (40-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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