Edit Profile (opens in new tab) Liu, Jianguo Co-Author Distance Author ID: liu.jian-guo Published as: Liu, Jian-Guo; Liu, J. G.; Liu, Jian-guo; Liu, Jianguo; Liu, J.-G. more...less Homepage: https://scholars.duke.edu/person/jian-guo.liu External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · dblp Documents Indexed: 265 Publications since 1993, including 21 Additional arXiv Preprints 5 Contributions as Editor Co-Authors: 158 Co-Authors with 254 Joint Publications 5,745 Co-Co-Authors all top 5 Co-Authors 0 single-authored 28 Gao, Yuan 25 Li, Lei 22 Degond, Pierre 16 Pego, Robert Leo 15 Zhou, Zhennan 14 Jin, Shi 13 Wang, Cheng 11 E, Weinan 10 Wang, Jinhuan 9 Lu, Jianfeng 8 Frouvelle, Amic 8 Wang, Li 8 Xin, Zhouping 7 Huang, Hui 7 Wang, Wei-Cheng 6 Feng, Yuanyuan 6 Liu, Jie 6 Liu, Zibu 6 Xu, Xiangsheng 5 Chen, Xiuqing 5 Gao, Yu 5 Johnston, Hans 5 Zhang, Yuan 4 Guo, Qiang 4 Marzuola, Jeremy Louis 4 Ringhofer, Christian A. 4 Wang, Guoyou 4 Xu, Xiaoqian 3 Chan, Francis H. Y. 3 Chertock, Alina E. 3 Lam, F. K. 3 Pendleton, Terrance 3 Qi, Di 3 Tang, Min 3 Tariq, Kalim U. 3 Wang, Ziheng 3 Witelski, Thomas P. 3 Xie, Yantong 3 Yang, Rong 2 Bian, Shen 2 Chae, Dongho 2 Chen, Gui-Qiang G. 2 Chen, Jingrun 2 Chen, Li 2 Cong, Wenting 2 Coquel, Frédéric 2 Duan, Yong 2 Goudon, Thierry 2 Herty, Michael Matthias 2 Huang, Yin-Liang 2 Ji, Hangjie 2 LeFloch, Philippe Gerard 2 Levermore, C. David 2 Li, Bo 2 Li, Qin 2 Li, Wuchen 2 Lin, Ping 2 Lu, Xiliang 2 Lu, Xinyang 2 Lu, Yulong 2 Ma, Zheng 2 Mieussens, Luc 2 Motsch, Sébastien 2 Nisar, Sana 2 Shu, Chi-Wang 2 Slepčev, Dejan 2 Tadmor, Eitan 2 Tang, Yijia 2 Tzavaras, Athanasios E. 2 Wang, Yuliang 2 Xu, Wenqing 2 Yan, Bokai 2 Zeng, Zhifang 2 Zhao, Yu 2 Zhou, Tao 1 Acheritogaray, Marion 1 Ai, Guo-Ping 1 Antman, Stuart S. 1 Badshah, Fazal 1 Baeder, James D. 1 Bao, Weizhu 1 Cai, Zhenhao 1 Carrillo de la Plata, José Antonio 1 Chainais-Hillairet, Claire 1 Chen, Kan 1 Chen, Ke 1 Chen, Zhong 1 Cherepanov, Vladislav V. 1 Chern, I-Liang 1 Childress, Stephen 1 Choi, Hwajeong 1 Craig, Katy 1 Dai, Shikun 1 Dang, Yanzhong 1 de Hoop, Maarten V. 1 Dou, Xu’an 1 Du, Jianqiang 1 Duraisamy, Karthikeyan 1 Engel, Maximilian 1 Engquist, Bjorn E. ...and 82 more Co-Authors all top 5 Serials 16 Journal of Computational Physics 15 Mathematics of Computation 14 SIAM Journal on Mathematical Analysis 13 Discrete and Continuous Dynamical Systems. Series B 13 Communications in Mathematical Sciences 8 SIAM Journal on Numerical Analysis 7 Quarterly of Applied Mathematics 7 Communications in Computational Physics 6 Physica D 6 Journal of Scientific Computing 6 Methods and Applications of Analysis 5 Journal of Statistical Physics 5 Journal of Nonlinear Science 5 Multiscale Modeling & Simulation 5 Kinetic and Related Models 4 Archive for Rational Mechanics and Analysis 4 Communications on Pure and Applied Mathematics 4 Nonlinearity 4 Journal of Differential Equations 4 Applied Mathematics Letters 3 Numerische Mathematik 3 Acta Applicandae Mathematicae 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Scientific Computing 3 Chaos 3 Annals of Mathematical Sciences and Applications 2 Communications in Mathematical Physics 2 International Journal for Numerical Methods in Fluids 2 Chinese Annals of Mathematics. Series B 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 SIAM Journal on Applied Mathematics 2 Calculus of Variations and Partial Differential Equations 2 Interfaces and Free Boundaries 2 International Journal of Pure and Applied Mathematics 2 Proceedings of Symposia in Applied Mathematics 2 Chinese Journal of Physics (Taipei) 2 Research in the Mathematical Sciences 1 Modern Physics Letters B 1 American Mathematical Monthly 1 Applicable Analysis 1 Computers and Fluids 1 Inverse Problems 1 Journal of Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Transport Theory and Statistical Physics 1 IEEE Transactions on Computers 1 Transactions of the American Mathematical Society 1 Parallel Computing 1 Applied Numerical Mathematics 1 Journal of Parallel and Distributed Computing 1 European Journal of Applied Mathematics 1 Signal Processing 1 IEEE Transactions on Signal Processing 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Review 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Physics of Fluids 1 Applied and Computational Harmonic Analysis 1 Discrete and Continuous Dynamical Systems 1 Matemática Contemporânea 1 Communications in Applied Analysis 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Nonlinear Dynamics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 International Journal of Modern Physics C 1 IEEE Transactions on Image Processing 1 EURASIP Journal on Applied Signal Processing 1 Communications on Pure and Applied Analysis 1 Journal of Applied Mathematics and Computing 1 Milan Journal of Mathematics 1 Journal of University of Electronic Science and Technology of China 1 International Journal of Geometric Methods in Modern Physics 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore 1 Series in Contemporary Applied Mathematics CAM 1 The European Physical Journal B. Condensed Matter and Complex Systems 1 Communications in Applied Mathematics and Computational Science 1 Inverse Problems and Imaging 1 RIMS Kôkyûroku Bessatsu 1 EURASIP Journal on Advances in Signal Processing 1 SIAM/ASA Journal on Uncertainty Quantification 1 Séminaire Laurent Schwartz. EDP et Applications 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Pure and Applied Analysis 1 Journal of Nonlinear, Complex and Data Science all top 5 Fields 153 Partial differential equations (35-XX) 95 Numerical analysis (65-XX) 93 Fluid mechanics (76-XX) 44 Statistical mechanics, structure of matter (82-XX) 37 Biology and other natural sciences (92-XX) 35 Probability theory and stochastic processes (60-XX) 17 Dynamical systems and ergodic theory (37-XX) 15 Mechanics of deformable solids (74-XX) 10 Ordinary differential equations (34-XX) 10 Computer science (68-XX) 9 Operations research, mathematical programming (90-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 General and overarching topics; collections (00-XX) 6 Statistics (62-XX) 6 Information and communication theory, circuits (94-XX) 5 Operator theory (47-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Real functions (26-XX) 4 Special functions (33-XX) 4 Integral transforms, operational calculus (44-XX) 4 Integral equations (45-XX) 4 Functional analysis (46-XX) 4 Mechanics of particles and systems (70-XX) 4 Systems theory; control (93-XX) 3 Geophysics (86-XX) 2 Combinatorics (05-XX) 2 Difference and functional equations (39-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Optics, electromagnetic theory (78-XX) 2 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Differential geometry (53-XX) 1 Astronomy and astrophysics (85-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 211 Publications have been cited 4,212 times in 2,856 Documents Cited by ▼ Year ▼ A simple proof of the Cucker-Smale flocking dynamics and mean-field limit. Zbl 1177.92003 Ha, Seung-Yeal; Liu, Jian-Guo 329 2009 A coupled chemotaxis-fluid model: global existence. Zbl 1236.92013 Liu, Jian-Guo; Lorz, Alexander 208 2011 Well-posedness for Hall-magnetohydrodynamics. Zbl 1297.35064 Chae, Dongho; Degond, Pierre; Liu, Jian-Guo 175 2014 Kinetic formulation and global existence for the Hall-magneto-hydrodynamics system. Zbl 1251.35076 Acheritogaray, Marion; Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo 172 2011 Projection method. I: Convergence and numerical boundary layers. Zbl 0842.76052 E, Weinan; Liu, Jian-Guo 122 1995 Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term. Zbl 1127.76343 Johnston, Hans; Liu, Jian-Guo 105 2004 Thin film epitaxy with or without slope selection. Zbl 1059.35059 Li, Bo; Liu, Jian-Guo 97 2003 Vorticity boundary condition and related isssues for finite difference schemes. Zbl 0847.76050 E, Weinan; Liu, Jian-Guo 79 1996 An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations. Zbl 1373.76284 Haack, Jeffrey; Jin, Shi; Liu, Jian-guo 74 2012 A high-order discontinuous Galerkin method for 2D incompressible flows. Zbl 0963.76069 Liu, Jian-Guo; Shu, Chi-Wang 67 2000 Essentially compact schemes for unsteady viscous incompressible flows. Zbl 0853.76045 E, Weinan; Liu, Jian-Guo 64 1996 Cauchy problems for Keller-Segel type time-space fractional diffusion equation. Zbl 1427.35329 Li, Lei; Liu, Jian-Guo; Wang, Lizhen 64 2018 Gauge method for viscous incompressible flows. Zbl 1160.76329 E, Weinan; Liu, Jian-Guo 62 2003 Macroscopic limits and phase transition in a system of self-propelled particles. Zbl 1275.35019 Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo 59 2013 Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent \(m > 0\). Zbl 1292.35061 Bian, Shen; Liu, Jian-Guo 57 2013 Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics. Zbl 1311.82017 Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo 57 2015 Random batch methods (RBM) for interacting particle systems. Zbl 1453.82065 Jin, Shi; Li, Lei; Liu, Jian-Guo 55 2020 Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. Zbl 1032.82038 Chainais-Hillairet, Claire; Liu, Jian-Guo; Peng, Yue-Jun 53 2003 A note on Aubin-Lions-Dubinskiĭ lemmas. Zbl 1326.46019 Chen, Xiuqing; Jüngel, Ansgar; Liu, Jian-Guo 51 2014 Dynamics in a kinetic model of oriented particles with phase transition. Zbl 1248.35097 Frouvelle, Amic; Liu, Jian-Guo 47 2012 Some compactness criteria for weak solutions of time fractional PDEs. Zbl 1403.35318 Li, Lei; Liu, Jian-Guo 47 2018 A generalized definition of Caputo derivatives and its application to fractional ODEs. Zbl 1401.26013 Li, Lei; Liu, Jian-Guo 45 2018 Hydrodynamic models of self-organized dynamics: derivation and existence theory. Zbl 1278.35153 Degond, Pierre; Liu, Jian-Guo; Motsch, Sebastien; Panferov, Vladislav 44 2013 Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate. Zbl 1131.35058 Liu, Jian-Guo; Liu, Jie; Pego, Robert L. 43 2007 Stable and accurate pressure approximation for unsteady incompressible viscous flow. Zbl 1307.76029 Liu, Jian-Guo; Liu, Jie; Pego, Robert L. 43 2010 Epitaxial growth without slope selection: energetics, coarsening, and dynamic scaling. Zbl 1123.35327 Li, Bo; Liu, Jian-Guo 42 2004 Convergence of gauge method for incompressible flow. Zbl 0968.76065 Wang, Cheng; Liu, Jian-Guo 40 2000 Finite difference schemes for incompressible flow based on local pressure boundary conditions. Zbl 1130.76409 Johnston, Hans; Liu, Jian-Guo 39 2002 A fourth-order scheme for incompressible Boussinesq equations. Zbl 1112.76051 Liu, Jian-Guo; Wang, Cheng; Johnston, Hans 39 2003 Accurate evaluation of electrostatics for macromolecules in solution. Zbl 1099.92500 Chern, I-Liang; Liu, Jian-Guo; Wang, Wei-Cheng 38 2003 Convergence of vortex methods for weak solutions to the \(2-D\) Euler equations with vortex sheet data. Zbl 0829.35098 Liu, Jian-Guo; Xin, Zhouping 37 1995 Characterization and regularity for axisymmetric solenoidal vector fields with application to Navier-Stokes equation. Zbl 1197.35195 Liu, Jian-Guo; Wang, Wei-Cheng 36 2009 Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit. Zbl 1220.65116 Liu, Jian-Guo; Mieussens, Luc 36 2010 Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations. Zbl 1383.65111 Liu, Jian-Guo; Wang, Li; Zhou, Zhennan 36 2018 Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition-based asymptotic-preserving method. Zbl 1375.65004 Jin, Shi; Liu, Jian-Guo; Ma, Zheng 34 2017 Mach-number uniform asymptotic-preserving gauge schemes for compressible flows. Zbl 1210.76135 Degond, P.; Jin, S.; Liu, J.-G. 32 2007 Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry. Zbl 1288.76093 Liu, Jian-Guo; Wang, Wei-Cheng 32 2004 Analysis of a fourth-order finite difference method for the incompressible Boussinesq equations. Zbl 1055.76042 Wang, Cheng; Liu, Jian-Guo; Johnston, Hans 31 2004 Multidimensional degenerate Keller-Segel system with critical diffusion exponent \(2n/(n+2)\). Zbl 1255.35034 Chen, Li; Liu, Jian-Guo; Wang, Jinhuan 31 2012 Stable discretization of magnetohydrodynamics in bounded domains. Zbl 1278.76127 Liu, Jian-Guo; Pego, Robert 30 2010 Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos. Zbl 1358.65073 Huang, Hui; Liu, Jian-Guo 29 2016 Large-scale dynamics of mean-field games driven by local Nash equilibria. Zbl 1295.91015 Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian 29 2014 The effects of numerical viscosities. I: Slowly moving shocks. Zbl 0858.76054 Jin, Shi; Liu, Jian-Guo 27 1996 Projection method. III: Spatial discretization on the staggered grid. Zbl 1058.76043 E, Weinan; Liu, Jian-Guo 25 2002 Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria. Zbl 1298.91104 Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian 24 2014 Projection method. II: Godunov-Ryabenki analysis. Zbl 0920.76056 E, Weinan; Liu, Jian-Guo 24 1996 Coagulation-fragmentation model for animal group-size statistics. Zbl 1382.92260 Degond, Pierre; Liu, Jian-Guo; Pego, Robert L. 23 2017 Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation. Zbl 1022.76039 Wang, Cheng; Liu, Jian-Guo 23 2002 Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on nonstaggered grids. Zbl 0901.76046 E, Weinan; Liu, Jian-Guo 23 1997 On generating functions of Hausdorff moment sequences. Zbl 1350.44003 Liu, Jian-Guo; Pego, Robert L. 22 2016 Convergence of a particle method and global weak solutions of a family of evolutionary PDEs. Zbl 1239.35120 Chertock, Alina; Liu, Jian-Guo; Pendleton, Terrance 21 2012 A degenerate \(p\)-Laplacian Keller-Segel model. Zbl 1364.35162 Cong, Wenting; Liu, Jian-Guo 20 2016 Macroscopic fluid models with localized kinetic upscaling effects. Zbl 1147.82331 Degond, Pierre; Liu, Jian-Guo; Mieussens, Luc 19 2006 Ultra-contractivity for Keller-Segel model with diffusion exponent \(m>1-2/d\). Zbl 1295.35271 Bian, Shen; Liu, Jian-Guo; Zou, Chen 19 2014 Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit. Zbl 1173.82032 Degond, Pierre; Liu, Jian-Guo; Vignal, Marie-Hélène 19 2008 Convergence of the point vortex method for 2-D vortex sheet. Zbl 0977.76069 Liu, Jian-Guo; Xin, Zhouping 19 2001 Fractional stochastic differential equations satisfying fluctuation-dissipation theorem. Zbl 1386.82053 Li, Lei; Liu, Jian-Guo; Lu, Jianfeng 18 2017 Evolution of wealth in a non-conservative economy driven by local Nash equilibria. Zbl 1353.91051 Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian 18 2014 Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows. Zbl 1130.76053 Liu, Jian-Guo; Wang, Wei-Cheng 18 2006 An energy-preserving MAC-Yee scheme for the incompressible MHD equation. Zbl 0999.76096 Liu, Jian-Guo; Wang, Wei-Cheng 18 2001 Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow. Zbl 1054.76025 Ghil, Michael; Liu, Jian-Guo; Wang, Cheng; Wang, Shouhong 18 2004 An accurate front capturing scheme for tumor growth models with a free boundary limit. Zbl 1395.65050 Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan 18 2018 Mean-field games and model predictive control. Zbl 1383.93029 Degond, Pierre; Herty, Michael; Liu, Jian-Guo 18 2017 Continuous and discrete one dimensional autonomous fractional ODEs. Zbl 1405.34008 Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo; Xu, Xiaoqian 18 2018 Propagation of chaos for large Brownian particle system with Coulomb interaction. Zbl 1355.82025 Liu, Jian-Guo; Yang, Rong 17 2016 Existence theorems for a multidimensional crystal surface model. Zbl 1355.35091 Liu, Jian-Guo; Xu, Xiangsheng 17 2016 Finite difference schemes for incompressible flows in the velocity-impulse density formulation. Zbl 0870.76048 E, Weinan; Liu, Jian-Guo 17 1997 Blow-up, zero \(\alpha\) limit and the Liouville type theorem for the Euler-poincaré equations. Zbl 1251.35075 Chae, Dongho; Liu, Jian-Guo 17 2012 Convergence of the random batch method for interacting particles with disparate species and weights. Zbl 1466.65011 Jin, Shi; Li, Lei; Liu, Jian-Guo 17 2021 A stochastic version of Stein variational gradient descent for efficient sampling. Zbl 1444.62043 Li, Lei; Li, Yingzhou; Liu, Jian-Guo; Liu, Zibu; Lu, Jianfeng 16 2020 On the diffusion approximation of nonconvex stochastic gradient descent. Zbl 1421.90121 Hu, Wenqing; Li, Chris Junchi; Li, Lei; Liu, Jian-Guo 16 2019 A random particle blob method for the Keller-Segel equation and convergence analysis. Zbl 1355.60092 Liu, Jian-Guo; Yang, Rong 16 2017 Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation. Zbl 0858.76073 Liu, Jian-Guo; Xin, Zhouping 15 1996 Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions. Zbl 0915.35069 LeFloch, Philippe G.; Liu, Jian-Guo 15 1999 Multiple-soliton solutions, soliton-type solutions and rational solutions for the \((3+1)\)-dimensional generalized shallow water equation in oceans, estuaries and impoundments. Zbl 1349.35058 Zeng, Zhi-Fang; Liu, Jian-Guo; Nie, Bin 14 2016 Gradient flow approach to an exponential thin film equation: global existence and latent singularity. Zbl 1442.35185 Gao, Yuan; Liu, Jian-Guo; Lu, Xin Yang 14 2019 Error estimate of a random particle blob method for the Keller-Segel equation. Zbl 1368.65207 Huang, Hui; Liu, Jian-Guo 14 2017 A note on \(L^\infty\)-bound and uniqueness to a degenerate Keller-Segel model. Zbl 1335.35103 Liu, Jian-Guo; Wang, Jinhuan 14 2016 Nonlinear stability of discrete shocks for systems of conservation laws. Zbl 0807.35087 Liu, Jian-Guo; Xin, Zhouping 14 1993 Simple finite element method in vorticity formulation for incompressible flows. Zbl 0977.76048 Liu, Jian-Guo; E, Weinan 14 2001 Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions. Zbl 1260.35231 Chen, Xiuqing; Liu, Jian-Guo 14 2013 On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system. Zbl 1466.35344 Huang, Hui; Liu, Jian-Guo; Pickl, Peter 14 2020 Partial regularity of weak solutions to a PDE system with cubic nonlinearity. Zbl 1383.35042 Liu, Jian-Guo; Xu, Xiangsheng 13 2018 Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime. Zbl 1377.35145 Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng 13 2017 The reconstruction of upwind fluxes for conservation laws: Its behavior in dynamic and steady state calculations. Zbl 0935.76048 Choi, Hwajeong; Liu, Jian-Guo 13 1998 Online learning in optical tomography: a stochastic approach. Zbl 1507.65304 Chen, Ke; Li, Qin; Liu, Jian-Guo 13 2018 Learning interacting particle systems: diffusion parameter estimation for aggregation equations. Zbl 1412.65171 Huang, Hui; Liu, Jian-Guo; Lu, Jianfeng 12 2019 Global existence for Nernst-Planck-Navier-Stokes system in \(\mathbb{R}^n\). Zbl 1464.35186 Liu, Jian-Guo; Wang, Jinhuan 12 2020 Global stability for solutions to the exponential PDE describing epitaxial growth. Zbl 1418.35215 Liu, Jian-Guo; Strain, Robert M. 12 2019 Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows. Zbl 1349.82046 Goudon, Thierry; Jin, Shi; Liu, Jian-Guo; Yan, Bokai 11 2013 On the mean field limit for Brownian particles with Coulomb interaction in 3D. Zbl 1431.82019 Li, Lei; Liu, Jian-Guo; Yu, Pu 11 2019 Long-time dynamics for a simple aggregation equation on the sphere. Zbl 1442.82031 Frouvelle, Amic; Liu, Jian-Guo 11 2019 Concepts and application of time-limiters to high resolution schemes. Zbl 1081.76582 Duraisamy, Karthikeyan; Baeder, James D.; Liu, Jian-Guo 11 2003 Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model. Zbl 1451.35074 Liu, Jian-Guo; Lu, Jianfeng; Margetis, Dionisios; Marzuola, Jeremy L. 11 2019 Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces. Zbl 1365.35174 Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng 10 2017 Elastic collisions among peakon solutions for the Camassa-Holm equation. Zbl 1326.35309 Chertock, Alina; Liu, Jian-Guo; Pendleton, Terrance 10 2015 Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions. Zbl 1422.76043 Liu, Jian-Guo; Liu, Jie; Pego, Robert L. 10 2009 Large oscillations arising in a dispersive numerical scheme. Zbl 0887.65098 Levermore, C. D.; Liu, Jian-Guo 10 1996 Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation. Zbl 1387.35024 Degond, Pierre; Liu, Jian-Guo 10 2012 Transition path theory for Langevin dynamics on manifolds: optimal control and data-driven solver. Zbl 1517.60087 Gao, Yuan; Li, Tiejun; Li, Xiaoguang; Liu, Jian-Guo 10 2023 The best constant for \(L^{\infty}\)-type Gagliardo-Nirenberg inequalities. Zbl 1534.39016 Liu, Jian-Guo; Wang, Jinhuan 1 2024 Master equations for finite state mean field games with nonlinear activations. Zbl 1537.49035 Gao, Yuan; Liu, Jian-Guo; Li, Wuchen 1 2024 Transition path theory for Langevin dynamics on manifolds: optimal control and data-driven solver. Zbl 1517.60087 Gao, Yuan; Li, Tiejun; Li, Xiaoguang; Liu, Jian-Guo 10 2023 Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions. Zbl 1509.82098 Gao, Yuan; Liu, Jian-Guo; Wu, Nan 6 2023 A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures. Zbl 1531.37056 Gao, Yuan; Liu, Jian-Guo 3 2023 A tumor growth model with autophagy: the reaction-(cross-)diffusion system and its free boundary limit. Zbl 1502.35178 Dou, Xu’an; Liu, Jian-Guo; Zhou, Zhennan 3 2023 A random batch method for efficient ensemble forecasts of multiscale turbulent systems. Zbl 07881240 Qi, Di; Liu, Jian-Guo 1 2023 Random walk approximation for irreversible drift-diffusion process on manifold: ergodicity, unconditional stability and convergence. Zbl 07738849 Gao, Yuan; Liu, Jian-Guo 1 2023 Large deviation principle and thermodynamic limit of chemical master equation via nonlinear semigroup. Zbl 1528.49026 Gao, Yuan; Liu, Jian-Guo 1 2023 On the equilibrium of the Poisson-Nernst-Planck-Bikermann model equipping with the steric and correlation effects. Zbl 1516.35427 Liu, Jian-Guo; Tang, Yijia; Zhao, Yu 1 2023 Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint. Zbl 1498.80011 Gao, Yuan; Liu, Jian-Guo 10 2022 Rigorous justification of the Fokker-Planck equations of neural networks based on an iteration perspective. Zbl 1496.35389 Liu, Jian-Guo; Wang, Ziheng; Zhang, Yuan; Zhou, Zhennan 5 2022 Nonlinear dynamics for different nonautonomous wave structures solutions of a 3D variable-coefficient generalized shallow water wave equation. Zbl 07851729 Liu, Jian-Guo; Osman, M. S. 4 2022 Multiple rogue wave solutions for the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation. Zbl 1540.35101 Liu, Jian-Guo; Zhao, Huan 4 2022 Projection method for droplet dynamics on groove-textured surface with merging and splitting. Zbl 1485.35433 Gao, Yuan; Liu, Jian-Guo 3 2022 Some random batch particle methods for the Poisson-Nernst-Planck and Poisson-Boltzmann equations. Zbl 1492.35371 Li, Lei; Liu, Jian-Guo; Tang, Yijia 2 2022 Existence of global weak solutions of \(p\)-Navier-Stokes equations. Zbl 1503.35136 Liu, Jian-Guo; Zhang, Zhaoyun 1 2022 Convergence of the random batch method for interacting particles with disparate species and weights. Zbl 1466.65011 Jin, Shi; Li, Lei; Liu, Jian-Guo 17 2021 A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration. Zbl 1515.65220 Hu, Jingwei; Liu, Jian-Guo; Xie, Yantong; Zhou, Zhennan 9 2021 Existence and incompressible limit of a tissue growth model with autophagy. Zbl 1473.35079 Liu, Jian-Guo; Xu, Xiangsheng 8 2021 Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space. Zbl 1471.35268 Gao, Yuan; Liu, Jian-Guo; Luo, Tao; Xiang, Yang 5 2021 Toward understanding the boundary propagation speeds in tumor growth models. Zbl 1472.35404 Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan 5 2021 Existence and rigidity of the vectorial Peierls-Nabarro model for dislocations in high dimensions. Zbl 1478.35199 Gao, Yuan; Liu, Jian-Guo; Liu, Zibu 5 2021 Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface. Zbl 1486.35345 Gao, Yuan; Liu, Jian-Guo 4 2021 Analysis of a fourth-order exponential PDE arising from a crystal surface jump process with metropolis-type transition rates. Zbl 1489.35270 Gao, Yuan; Katsevich, Anya E.; Liu, Jian-Guo; Lu, Jianfeng; Marzuola, Jeremy L. 3 2021 Large time behavior, bi-Hamiltonian structure, and kinetic formulation for a complex Burgers equation. Zbl 1456.35033 Gao, Yu; Gao, Yuan; Liu, Jian-Guo 3 2021 Inbetweening auto-animation via Fokker-Planck dynamics and thresholding. Zbl 1507.68331 Gao, Yuan; Jin, Guangzhen; Liu, Jian-Guo 2 2021 Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: derivations and computations. Zbl 1483.76063 Gao, Yuan; Liu, Jian-Guo 1 2021 Field model for complex ionic fluids: analytical properties and numerical investigation. Zbl 1473.35601 Liu, Jian-Guo; Wang, Jinhuan; Zhao, Yu; Zhou, Zhennan 1 2021 Random batch methods (RBM) for interacting particle systems. Zbl 1453.82065 Jin, Shi; Li, Lei; Liu, Jian-Guo 55 2020 A stochastic version of Stein variational gradient descent for efficient sampling. Zbl 1444.62043 Li, Lei; Li, Yingzhou; Liu, Jian-Guo; Liu, Zibu; Lu, Jianfeng 16 2020 On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system. Zbl 1466.35344 Huang, Hui; Liu, Jian-Guo; Pickl, Peter 14 2020 Global existence for Nernst-Planck-Navier-Stokes system in \(\mathbb{R}^n\). Zbl 1464.35186 Liu, Jian-Guo; Wang, Jinhuan 12 2020 Large time behaviors of upwind schemes and \(B\)-schemes for Fokker-Planck equations on \(\mathbb{R}\) by jump processes. Zbl 1442.65214 Li, Lei; Liu, Jian-Guo 8 2020 Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects. Zbl 1443.35085 Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng; Marzuola, Jeremy L. 7 2020 A note on parametric Bayesian inference via gradient flows. Zbl 1465.76075 Gao, Yuan; Liu, Jian-Guo 7 2020 Uniform-in-time weak error analysis for stochastic gradient descent algorithms via diffusion approximation. Zbl 1440.60073 Feng, Yuanyuan; Gao, Tingran; Li, Lei; Liu, Jian-Guo; Lu, Yulong 3 2020 Long time behavior of dynamic solution to Peierls-Nabarro dislocation model. Zbl 1448.35044 Gao, Yuan; Liu, Jian-Guo 3 2020 A class of functional inequalities and their applications to fourth-order nonlinear parabolic equations. Zbl 1462.35104 Liu, Jian-Guo; Xu, Xiangsheng 1 2020 On the diffusion approximation of nonconvex stochastic gradient descent. Zbl 1421.90121 Hu, Wenqing; Li, Chris Junchi; Li, Lei; Liu, Jian-Guo 16 2019 Gradient flow approach to an exponential thin film equation: global existence and latent singularity. Zbl 1442.35185 Gao, Yuan; Liu, Jian-Guo; Lu, Xin Yang 14 2019 Learning interacting particle systems: diffusion parameter estimation for aggregation equations. Zbl 1412.65171 Huang, Hui; Liu, Jian-Guo; Lu, Jianfeng 12 2019 Global stability for solutions to the exponential PDE describing epitaxial growth. Zbl 1418.35215 Liu, Jian-Guo; Strain, Robert M. 12 2019 On the mean field limit for Brownian particles with Coulomb interaction in 3D. Zbl 1431.82019 Li, Lei; Liu, Jian-Guo; Yu, Pu 11 2019 Long-time dynamics for a simple aggregation equation on the sphere. Zbl 1442.82031 Frouvelle, Amic; Liu, Jian-Guo 11 2019 Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model. Zbl 1451.35074 Liu, Jian-Guo; Lu, Jianfeng; Margetis, Dionisios; Marzuola, Jeremy L. 11 2019 Well-posedness and derivative blow-up for a dispersionless regularized shallow water system. Zbl 1428.35375 Liu, Jian-Guo; Pego, Robert L.; Pu, Yue 9 2019 Least action principles for incompressible flows and geodesics between shapes. Zbl 1428.35376 Liu, Jian-Guo; Pego, Robert L.; Slepčev, Dejan 9 2019 Propagation of chaos for the Keller-Segel equation with a logarithmic cut-off. Zbl 1442.35199 Liu, Jian-Guo; Yang, Rong 8 2019 Patched peakon weak solutions of the modified Camassa-Holm equation. Zbl 1448.37087 Gao, Yu; Li, Lei; Liu, Jian-Guo 8 2019 A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows. Zbl 07105241 Li, Lei; Liu, Jian-Guo 7 2019 Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics. Zbl 1418.35225 Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan 6 2019 On local singularities in ideal potential flows with free surface. Zbl 1428.76029 Liu, Jian-Guo; Pego, Robert L. 4 2019 On the rate of convergence of empirical measure in \(\infty \)-Wasserstein distance for unbounded density function. Zbl 1447.60008 Liu, Anning; Liu, Jian-Guo; Lu, Yulong 3 2019 Self-similar spreading in a merging-splitting model of animal group size. Zbl 1420.92095 Liu, Jian-Guo; Niethammer, B.; Pego, Robert L. 2 2019 Cauchy problems for Keller-Segel type time-space fractional diffusion equation. Zbl 1427.35329 Li, Lei; Liu, Jian-Guo; Wang, Lizhen 64 2018 Some compactness criteria for weak solutions of time fractional PDEs. Zbl 1403.35318 Li, Lei; Liu, Jian-Guo 47 2018 A generalized definition of Caputo derivatives and its application to fractional ODEs. Zbl 1401.26013 Li, Lei; Liu, Jian-Guo 45 2018 Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations. Zbl 1383.65111 Liu, Jian-Guo; Wang, Li; Zhou, Zhennan 36 2018 An accurate front capturing scheme for tumor growth models with a free boundary limit. Zbl 1395.65050 Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan 18 2018 Continuous and discrete one dimensional autonomous fractional ODEs. Zbl 1405.34008 Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo; Xu, Xiaoqian 18 2018 Partial regularity of weak solutions to a PDE system with cubic nonlinearity. Zbl 1383.35042 Liu, Jian-Guo; Xu, Xiangsheng 13 2018 Online learning in optical tomography: a stochastic approach. Zbl 1507.65304 Chen, Ke; Li, Qin; Liu, Jian-Guo 13 2018 Semigroups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations. Zbl 1417.60065 Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo 10 2018 A note on deconvolution with completely monotone sequences and discrete fractional calculus. Zbl 1476.47029 Li, Lei; Liu, Jian-Guo 9 2018 The modified Camassa-Holm equation in Lagrangian coordinates. Zbl 1404.35105 Gao, Yu; Liu, Jian-Guo 8 2018 Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface. Zbl 1401.35204 Gao, Yuan; Liu, Jian-Guo; Lu, Xin Yang; Xu, Xiangsheng 7 2018 A dispersive regularization for the modified Camassa-Holm equation. Zbl 1403.35075 Gao, Yu; Li, Lei; Liu, Jian-Guo 7 2018 A note on one-dimensional time fractional ODEs. Zbl 1503.34015 Feng, Yuanyuan; Li, Lei; Liu, Jian-Guo; Xu, Xiaoqian 5 2018 A vicinal surface model for epitaxial growth with logarithmic free energy. Zbl 1403.35123 Gao, Yuan; Ji, Hangjie; Liu, Jian-Guo; Witelski, Thomas P. 3 2018 \(p\)-Euler equations and \(p\)-Navier-Stokes equations. Zbl 1384.35093 Li, Lei; Liu, Jian-Guo 2 2018 Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws. Zbl 1384.65052 Coquel, Frédéric; Jin, Shi; Liu, Jian-Guo; Wang, Li 1 2018 Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition-based asymptotic-preserving method. Zbl 1375.65004 Jin, Shi; Liu, Jian-Guo; Ma, Zheng 34 2017 Coagulation-fragmentation model for animal group-size statistics. Zbl 1382.92260 Degond, Pierre; Liu, Jian-Guo; Pego, Robert L. 23 2017 Fractional stochastic differential equations satisfying fluctuation-dissipation theorem. Zbl 1386.82053 Li, Lei; Liu, Jian-Guo; Lu, Jianfeng 18 2017 Mean-field games and model predictive control. Zbl 1383.93029 Degond, Pierre; Herty, Michael; Liu, Jian-Guo 18 2017 A random particle blob method for the Keller-Segel equation and convergence analysis. Zbl 1355.60092 Liu, Jian-Guo; Yang, Rong 16 2017 Error estimate of a random particle blob method for the Keller-Segel equation. Zbl 1368.65207 Huang, Hui; Liu, Jian-Guo 14 2017 Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime. Zbl 1377.35145 Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng 13 2017 Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces. Zbl 1365.35174 Gao, Yuan; Liu, Jian-Guo; Lu, Jianfeng 10 2017 Continuum dynamics of the intention field under weakly cohesive social interaction. Zbl 1362.82033 Degond, Pierre; Liu, Jian-Guo; Merino-Aceituno, Sara; Tardiveau, Thomas 9 2017 Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions. Zbl 1371.35142 Liu, Jian-Guo; Xu, Xiangsheng 9 2017 Explicit and implicit TVD schemes for conservation laws with Caputo derivatives. Zbl 1371.65083 Liu, Jian-Guo; Ma, Zheng; Zhou, Zhennan 7 2017 Global convergence of a sticky particle method for the modified Camassa-Holm equation. Zbl 1458.35117 Gao, Yu; Liu, Jian-Guo 7 2017 Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis. Zbl 1390.35136 Huang, Hui; Liu, Jian-Guo 6 2017 A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation. Zbl 1357.35176 Liu, Jian-Guo; Wang, Jinhuan 3 2017 Uniform \(L^{\infty}\) boundedness for a degenerate parabolic-parabolic Keller-Segel model. Zbl 1360.35106 Cong, Wenting; Liu, Jian-Guo 3 2017 Global existence for a thin film equation with subcritical mass. Zbl 1360.35183 Liu, Jian-Guo; Wang, Jinhuan 3 2017 Global existence of solutions to a tear film model with locally elevated evaporation rates. Zbl 1376.76008 Gao, Yuan; Ji, Hangjie; Liu, Jian-Guo; Witelski, Thomas P. 1 2017 Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos. Zbl 1358.65073 Huang, Hui; Liu, Jian-Guo 29 2016 On generating functions of Hausdorff moment sequences. Zbl 1350.44003 Liu, Jian-Guo; Pego, Robert L. 22 2016 A degenerate \(p\)-Laplacian Keller-Segel model. Zbl 1364.35162 Cong, Wenting; Liu, Jian-Guo 20 2016 Propagation of chaos for large Brownian particle system with Coulomb interaction. Zbl 1355.82025 Liu, Jian-Guo; Yang, Rong 17 2016 Existence theorems for a multidimensional crystal surface model. Zbl 1355.35091 Liu, Jian-Guo; Xu, Xiangsheng 17 2016 Multiple-soliton solutions, soliton-type solutions and rational solutions for the \((3+1)\)-dimensional generalized shallow water equation in oceans, estuaries and impoundments. Zbl 1349.35058 Zeng, Zhi-Fang; Liu, Jian-Guo; Nie, Bin 14 2016 A note on \(L^\infty\)-bound and uniqueness to a degenerate Keller-Segel model. Zbl 1335.35103 Liu, Jian-Guo; Wang, Jinhuan 14 2016 On a Schrödinger-Landau-Lifshitz system: variational structure and numerical methods. Zbl 1352.65388 Chen, Jingrun; Liu, Jian-Guo; Zhou, Zhennan 9 2016 Refined hyper-contractivity and uniqueness for the Keller-Segel equations. Zbl 1330.35040 Liu, Jian-Guo; Wang, Jinhuan 9 2016 Exact periodic cross-kink wave solutions for the new \((2+1)\)-dimensional KdV equation in fluid flows and plasma physics. Zbl 1378.35270 Liu, Jian-Guo; Du, Jian-Qiang; Zeng, Zhi-Fang; Ai, Guo-Ping 7 2016 Detecting community structure in directed networks via multiple eigenvectors. Zbl 1374.05213 Yang, Kai; Guo, Qiang; Liu, Xiaolu; Liu, Jianguo 1 2016 ...and 111 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,518 Authors 117 Liu, Jianguo 101 Ha, Seung-Yeal 55 Degond, Pierre 50 Jin, Shi 44 Carrillo de la Plata, José Antonio 40 Wang, Cheng 35 Shen, Jie 30 Choi, Young-Pil 28 Kim, Jeongho 27 Li, Lei 27 Yang, Xiaofeng 26 Liu, Yicheng 23 Winkler, Michael 23 Xiang, Zhaoyin 22 Chen, Wenbin 22 Pareschi, Lorenzo 21 Gao, Yuan 20 Zhou, Zhennan 19 Rebholz, Leo Gregory 19 Zhang, Xiongtao 18 Zhou, Yong 17 Fan, Jishan 17 Ko, Dongnam 17 Liu, Chun 17 Zhang, Qian 17 Zheng, Jiashan 16 Feng, Xinlong 16 Jüngel, Ansgar 16 Liu, Zuhan 16 Tadmor, Eitan 16 Wang, Li 15 Ahn, Hyunjin 15 Huang, Hui 15 Kim, Doheon 15 Shim, Woojoo 14 Chen, Li 14 Kim, Dohyun 14 Qiao, Zhonghua 14 Zhou, Yong 13 Chae, Dongho 13 Xue, Xiaoping 12 Dai, Mimi 12 Dimarco, Giacomo 12 He, Yinnian 12 Liu, Liu 12 Nguyen Huy Tuan 12 Park, Jinyeong 12 Qiu, Jingmei 12 Wise, Steven M. 12 Xu, Xiangsheng 12 Zhou, Ling 11 Albi, Giacomo 11 Chainais-Hillairet, Claire 11 Frouvelle, Amic 11 Gao, Yu 11 Hou, Thomas Yizhao 11 Kang, Kyungkeun 11 Kang, Moon-Jin 11 Li, Qin 11 Schütz, Jochen 11 Si, Zhiyong 11 Tan, Changhui 11 Wang, Xiao 11 Xiong, Tao 11 Yamazaki, Kazuo 10 Bian, Shen 10 Goudon, Thierry 10 Herty, Michael Matthias 10 Jin, Chunyin 10 Jung, Jinwook 10 Li, Bin 10 Lu, Jianfeng 10 Pego, Robert Leo 10 Peszek, Jan 10 Shu, Ruiwen 10 Shvydkoy, Roman V. 10 Wang, Jinhuan 10 Xin, Zhouping 10 Zhang, Zhengru 10 Zhao, Xiaopeng 9 Bae, Hyeong-Ohk 9 Cancès, Clément 9 Diez, Antoine 9 Li, Wuchen 9 Li, Zhilin 9 Li, Zhuchun 9 Perthame, Benoît 9 Tang, Tao 9 Wang, Xiaoming 9 Wang, Yulan 9 Zanella, Mattia 9 Zhang, Guodong 8 Bellomo, Nicola 8 Burger, Martin 8 Dong, Jiu-Gang 8 Guermond, Jean-Luc 8 Jin, Chunhua 8 Jiu, Quansen 8 Layton, William J. 8 Merino-Aceituno, Sara ...and 3,418 more Authors all top 5 Cited in 319 Serials 279 Journal of Computational Physics 131 Journal of Differential Equations 101 Journal of Scientific Computing 87 M\(^3\)AS. 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Second Series 5 Journal of Numerical Mathematics 5 Chinese Journal of Physics (Taipei) 5 Advances in Applied Mathematics and Mechanics 5 AIMS Mathematics ...and 219 more Serials all top 5 Cited in 47 Fields 1,796 Partial differential equations (35-XX) 1,252 Fluid mechanics (76-XX) 1,050 Numerical analysis (65-XX) 631 Biology and other natural sciences (92-XX) 354 Statistical mechanics, structure of matter (82-XX) 151 Probability theory and stochastic processes (60-XX) 146 Ordinary differential equations (34-XX) 98 Mechanics of deformable solids (74-XX) 97 Dynamical systems and ergodic theory (37-XX) 84 Systems theory; control (93-XX) 80 Calculus of variations and optimal control; optimization (49-XX) 72 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 64 Real functions (26-XX) 52 Mechanics of particles and systems (70-XX) 46 Optics, electromagnetic theory (78-XX) 42 Computer science (68-XX) 40 Operations research, mathematical programming (90-XX) 39 Operator theory (47-XX) 39 Quantum theory (81-XX) 37 Integral equations (45-XX) 35 Classical thermodynamics, heat transfer (80-XX) 25 Geophysics (86-XX) 23 Statistics (62-XX) 22 Functional analysis (46-XX) 16 Combinatorics (05-XX) 14 Special functions (33-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Approximations and expansions (41-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 13 Astronomy and astrophysics (85-XX) 12 Integral transforms, operational calculus (44-XX) 12 Global analysis, analysis on manifolds (58-XX) 10 Functions of a complex variable (30-XX) 8 Information and communication theory, circuits (94-XX) 7 General and overarching topics; collections (00-XX) 7 Difference and functional equations (39-XX) 7 Differential geometry (53-XX) 6 Measure and integration (28-XX) 4 Number theory (11-XX) 3 Potential theory (31-XX) 1 History and biography (01-XX) 1 Nonassociative rings and algebras (17-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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