Edit Profile (opens in new tab) Liu, Hailiang Compute Distance To: Compute Author ID: liu.hailiang Published as: Liu, Hailiang; Liu, H.; Liu, Hai-liang more...less Documents Indexed: 204 Publications since 1976 2 Further Contributions Co-Authors: 75 Co-Authors with 134 Joint Publications 2,909 Co-Co-Authors all top 5 Co-Authors 23 single-authored 9 Wang, Jinghua 9 Wang, Zhongming 8 Huang, Yunqing 8 Tadmor, Eitan 8 Yi, Nianyu 8 Yin, Peimeng 7 Warnecke, Gerald G. 6 Yu, Hui 5 Bhatnagar, Manas 5 Cai, Wenli 5 Li, Tong 5 Osher, Stanley Joel 4 Jiang, Yi 4 Jin, Shi 4 Maimaitiyiming, Wumaier 4 Ralston, James V. 4 Yang, Tong 3 Jabin, Pierre-Emmanuel 3 Lee, Yongki 3 Pollack, Michael 3 Runborg, Olof 3 Shin, Jaemin 3 Tanushev, Nicolay M. 3 Tsai, Yen-Hsi Richard 3 Wang, Zikun 3 Yan, Jue 2 Bernussou, Jacques 2 Chen, Gui-Qiang G. 2 Cheng, Li-Tien 2 Degond, Pierre 2 Hadji, Layachi 2 Krishnan, Sreedevi 2 Lu, Wenying 2 Marella, Saikrishna V. 2 Pan, Jun 2 Pryporov, Maksym 2 Saran, Haseena 2 Schreiber, Willard C. 2 Udaykumar, Holavanahalli S. 2 Wen, Hairui 1 Akulichev, Victor A. 1 Aten, Charlotte 1 Ates, Muzaffer 1 Axhausen, Kay W. 1 Ayachi, B. 1 Bajcinca, Naim 1 Bathe, Klaus-Jürgen 1 Bau, E. 1 Bazargan-Sabet, B. 1 Bressan, Alberto 1 Butterfaß, J. 1 Cao, Waixiang 1 Chanchole, S. 1 Chui, E. 1 Cleary, Michael P. 1 Davulcu, Hasan 1 Desai, Chandra S. 1 Di Francesco, Marco 1 Dirr, Bodo 1 Engelberg, Shlomo 1 Fan, Haitao 1 Fan, Yuanxun 1 Fellner, Klemens 1 Feng, Xiaobing 1 Fox, Rodney O. 1 Garg, Hari Krishna 1 Gröpler, Robin 1 Ha, Tae Gab 1 Huang, Yuxia 1 Huo, Xiaokai 1 Ikehata, Masaru 1 Iosevich, Alex 1 Katz, Casimir 1 Knoch, S. 1 Kobayashi, Shoichi 1 Kolippakkam, D. 1 Kunik, Matthias 1 Levermore, C. David 1 Liang, Fugang 1 Liao, Guojun 1 Lien, Fue-Sang 1 Liu, Chun 1 Ma, Shu 1 MacKinnon, I. 1 Maimon, Shir 1 Markowich, Peter Alexander 1 McCartney, C. J. 1 Mehl, Michael J. 1 Meusel, P. 1 Mira, Christian 1 Mu, S. Y. 1 Mühlhaus, Hans-Bernd 1 Natalini, Roberto 1 Nguyen, Hung Viet 1 Nilson, Robert H. 1 Nishimura, Naoshi 1 Nonami, Kenzo 1 Pakianathan, Jonathan 1 Panagiotopoulos, Panagiotis D. 1 Pande, Gyan N. ...and 43 more Co-Authors all top 5 Serials 25 Journal of Computational Physics 8 Mathematics of Computation 8 Journal of Differential Equations 8 Journal of Scientific Computing 8 Communications in Computational Physics 6 SIAM Journal on Numerical Analysis 6 Physica D 6 Applied Mathematics Letters 6 SIAM Journal on Scientific Computing 6 Communications in Mathematical Sciences 5 SIAM Journal on Mathematical Analysis 4 Journal of Computational and Applied Mathematics 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Methods and Applications of Analysis 4 Discrete and Continuous Dynamical Systems 3 International Journal of Solids and Structures 3 Numerische Mathematik 3 Numerical Methods for Partial Differential Equations 3 SIAM Journal on Applied Mathematics 3 Journal of Hyperbolic Differential Equations 2 Computers and Structures 2 International Journal for Numerical Methods in Fluids 2 Molecular Simulation 2 Indiana University Mathematics Journal 2 Acta Mathematica Hungarica 2 Japan Journal of Industrial and Applied Mathematics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Multiscale Modeling & Simulation 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Advances and Applications in Fluid Mechanics 1 Communications in Mathematical Physics 1 IMA Journal of Numerical Analysis 1 International Journal of Control 1 International Journal of Non-Linear Mechanics 1 International Journal of Systems Science 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Journal of Sound and Vibration 1 Mathematical Notes 1 Nonlinearity 1 Transport Theory and Statistical Physics 1 Wave Motion 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Fuzzy Sets and Systems 1 International Journal for Numerical Methods in Engineering 1 Journal of Functional Analysis 1 Mechanics Research Communications 1 Siberian Mathematical Journal 1 Mathematica Numerica Sinica 1 Acta Mathematicae Applicatae Sinica 1 Circuits, Systems, and Signal Processing 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Annals of Differential Equations 1 Asymptotic Analysis 1 Signal Processing 1 Systems Science and Mathematical Sciences 1 Numerical Algorithms 1 Applied Mathematical Modelling 1 Communications in Partial Differential Equations 1 Communications in Statistics. Simulation and Computation 1 Acta Mathematica Scientia 1 Journal of Partial Differential Equations 1 Advances in Engineering Software 1 Applied Mathematics. Series A (Chinese Edition) 1 Acustica - Acta Acustica 1 Journal of Vibration and Control 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Mechanism and Machine Theory 1 Flow, Turbulence and Combustion 1 Journal of Nonlinear Mathematical Physics 1 Communications on Pure and Applied Analysis 1 Communications in Information and Systems 1 Quantum Information Processing 1 Journal of Cosmology and Astroparticle Physics 1 Iranian Journal of Fuzzy Systems 1 Networks and Heterogeneous Media 1 Quantum Studies: Mathematics and Foundations 1 Annals of Applied Mathematics all top 5 Fields 135 Partial differential equations (35-XX) 89 Numerical analysis (65-XX) 46 Fluid mechanics (76-XX) 21 Statistical mechanics, structure of matter (82-XX) 15 Biology and other natural sciences (92-XX) 12 Mechanics of deformable solids (74-XX) 7 Quantum theory (81-XX) 6 Operations research, mathematical programming (90-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Mechanics of particles and systems (70-XX) 5 Optics, electromagnetic theory (78-XX) 4 Ordinary differential equations (34-XX) 4 Approximations and expansions (41-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Systems theory; control (93-XX) 3 Group theory and generalizations (20-XX) 3 Integral equations (45-XX) 3 Computer science (68-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Number theory (11-XX) 2 Difference and functional equations (39-XX) 2 Convex and discrete geometry (52-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Abstract harmonic analysis (43-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 147 Publications have been cited 1,611 times in 898 Documents Cited by ▼ Year ▼ Formation of \(\delta\)-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. Zbl 1038.35035Chen, Gui-Qiang; Liu, Hailiang 196 2003 Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids. Zbl 1098.76603Chen, Gui-Qiang; Liu, Hailiang 99 2004 The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227Liu, Hailiang; Yan, Jue 93 2009 Sharp interface Cartesian grid method. I: An easily implemented technique for 3D moving boundary computations. Zbl 1154.76359Marella, S.; Krishnan, S.; Liu, H.; Udaykumar, H. S. 75 2005 The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200Liu, Hailiang; Yan, Jue 72 2010 Critical thresholds in Euler-Poisson equations. Zbl 0989.35110Engelberg, Shlomo; Liu, Hailiang; Tadmor, Eitan 58 2001 Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure. Zbl 1005.74033Liu, H.; Wang, Z. K.; Wang, T. J. 41 2001 Critical thresholds in a convolution model for nonlinear conservation laws. Zbl 1002.35085Liu, Hailiang; Tadmor, Eitan 39 2001 Spectral dynamics of the velocity gradient field in restricted flows. Zbl 1031.76006Liu, Hailiang; Tadmor, Eitan 38 2002 A free energy satisfying finite difference method for Poisson-Nernst-Planck equations. Zbl 1349.65317Liu, Hailiang; Wang, Zhongming 38 2014 Computational high-frequency wave propagation using the level set method with applications to the semi-classical limit of Schrödinger equations. Zbl 1084.35066Cheng, Li-Tien; Liu, Hailiang; Osher, Stanley 38 2003 A numerical study of insect flight. Zbl 0929.76092Liu, H.; Kawachi, K. 36 1998 Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation. Zbl 1072.65132Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Yen-Hsi Richard 35 2005 Sharp interface Cartesian grid method. II: A technique for simulating droplet interactions with surfaces of arbitrary shape. Zbl 1154.76358Liu, H.; Krishnan, S.; Marella, S.; Udaykumar, H. S. 35 2005 A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. Zbl 1092.65083Liu, Hailiang; Yan, Jue 32 2006 Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential. Zbl 1092.76007Liu, Hailiang; Zhang, Hui; Zhang, Pingwen 31 2005 Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141Liu, Hailiang 31 2015 A numerical study of undulatory swimming. Zbl 0958.76099Liu, H.; Kawachi, K. 31 1999 Rotation prevents finite-time breakdown. Zbl 1098.76643Liu, Hailiang; Tadmor, Eitan 31 2004 Critical thresholds in 2D restricted Euler-Poisson equations. Zbl 1073.35187Liu, Hailiang; Tadmor, Eitan 31 2003 A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect. Zbl 1297.65122Yi, Nianyu; Huang, Yunqing; Liu, Hailiang 29 2013 A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021Liu, Hailiang; Wang, Zhongming 25 2017 Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin 24 2017 Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069Liu, Hailiang 23 2006 Error estimates for Gaussian beam superpositions. Zbl 1277.35236Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M. 23 2013 A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462Liu, Hailiang; Yi, Nianyu 20 2016 Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358Lu, Wenying; Huang, Yunqing; Liu, Hailiang 20 2015 Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems. Zbl 1098.65094Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Richard 20 2005 A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177Liu, Hailiang; Ploymaklam, Nattapol 19 2015 Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038Liu, Hailiang; Yu, Hui 18 2014 The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143Liu, Hailiang; Yu, Hui 17 2015 Entropy-based fuzzy clustering and fuzzy modeling. Zbl 1147.62348Yao, J.; Dash, M.; Tan, S. T.; Liu, H. 14 2000 Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws. Zbl 1039.35063Liu, Hailiang 14 2003 Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372Liu, Hailiang; Yin, Peimeng 14 2019 An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158Liu, Hailiang; Wang, Zhongming 14 2016 Multi-valued solution and level set methods in computational high frequency wave propagation. Zbl 1120.65110Liu, H.; Osher, S.; Tsai, R. 13 2006 Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420Lee, Yongki; Liu, Hailiang 12 2015 Stability of a relaxation model with a nonconvex flux. Zbl 0961.35017Liu, Hailiang; Wang, Jinghua; Yang, Tong 12 1998 Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031Liu, Hailiang; Ralston, James 12 2010 Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009Huang, Yunqing; Liu, Hailiang; Yi, Nianyu 12 2012 Kinetic models for polymers with inertial effects. Zbl 1183.76614Degond, Pierre; Liu, Hailiang 12 2009 Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062Li, Tong; Liu, Hailiang 11 2009 Decay rate for travelling waves of a relaxation model. Zbl 0908.35074Liu, Hailiang; Woo, Ching Wah; Yang, Tong 10 1997 A note on harmonic maps. Zbl 0996.58507Liu, H.; Liao, Guojun 10 1996 On discreteness of the Hopf equation. Zbl 1149.65071Liu, Hai-liang 10 2008 An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321Liu, Hailiang; Xing, Yulong 10 2016 A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168Liu, Hailiang; Yin, Peimeng 10 2018 Convergence rates for relaxation schemes approximating conservation laws. Zbl 0954.35108Liu, Hailiang; Warnecke, Gerald 10 2000 Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. Zbl 1395.76047Degond, P.; Liu, H.; Savelief, D.; Vignal, M.-H. 10 2012 An entropy satisfying conservative method for the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model. Zbl 1422.74097Liu, Hailiang; Yu, Hui 10 2012 KdV dynamics in the plasma-sheath transition. Zbl 1060.76137Liu, Hailiang; Slemrod, M. 9 2004 Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations. Zbl 1416.65293Jiang, Yi; Liu, Hailiang 9 2018 Stability of a traffic flow model with nonconvex relaxation. Zbl 1099.35156Li, Tong; Liu, Hailiang 8 2005 Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284Liu, Hailiang; Ralston, James 8 2010 The \(L^p\) stability of relaxation rarefaction profiles. Zbl 0988.35113Liu, Hailiang 8 2001 Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 1471.35277Liu, Hailiang; Maimaitiyiming, Wumaier 8 2021 A level set framework for capturing multi-valued solutions of nonlinear first-order equations. Zbl 1109.65080Liu, Hailiang; Cheng, Li-Tien; Osher, Stanley 7 2006 Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461Liu, Hailiang; Pollack, Michael 7 2014 Global regularity of the 4D restricted Euler equations. Zbl 1193.37123Liu, Hailiang; Tadmor, Eitan; Wei, Dongming 7 2010 Tiling sets and spectral sets over finite fields. Zbl 1376.52038Aten, C.; Ayachi, B.; Bau, E.; FitzPatrick, D.; Iosevich, A.; Liu, H.; Lott, A.; MacKinnon, I.; Maimon, S.; Nan, S.; Pakianathan, J.; Petridis, G.; Rojas Mena, C.; Sheikh, A.; Tribone, T.; Weill, J.; Yu, C. 7 2017 A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158Huang, Yunqing; Liu, Hailiang; Yi, Nianyu 6 2014 Robust control of robotic manipulators based on integral sliding mode. Zbl 1154.93344Shi, J.; Liu, H.; Bajcinca, N. 6 2008 An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162Yin, Peimeng; Huang, Yunqing; Liu, Hailiang 6 2014 On invariant-preserving finite difference schemes for the Camassa-Holm equation and the two-component Camassa-Holm system. Zbl 1388.65059Liu, Hailiang; Pendleton, Terrance 6 2016 Global well-posedness for the microscopic FENE model with a sharp boundary condition. Zbl 1233.35109Liu, Hailiang; Shin, Jaemin 6 2012 Diffusion limit of a hyperbolic system with relaxation. Zbl 0922.35086Jin, Shi; Liu, Hailiang 6 1998 Semiclassical limit of the nonlinear Schrödinger-Poisson equation with subcritical initial data. Zbl 1166.35374Liu, Hailiang; Tadmor, Eitan 6 2002 Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006Li, Tong; Liu, Hailiang 6 2008 A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063di Francesco, Marco; Fellner, Klemens; Liu, Hailiang 6 2008 Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175Liu, Hailiang; Yin, Zhaoyang 6 2010 Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145Bhatnagar, Manas; Liu, Hailiang 6 2020 A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations. Zbl 1140.81399Liu, Hailiang; Wang, Zhongming 5 2007 Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101Liu, Hailiang 5 2007 Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations. Zbl 1146.78012Liu, Hailiang; Wang, Zhongming 5 2007 Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250Lee, Yongki; Liu, Hailiang 5 2015 Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356Liu, Hailiang; Pollack, Michael 5 2016 Boundary conditions for the microscopic FENE models. Zbl 1147.76003Liu, Chun; Liu, Hailiang 5 2008 Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141Liu, Hailiang; Wang, Zhongming 5 2008 Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation. Zbl 1362.37161Levermore, C. David; Liu, Hailiang; Pego, Robert L. 5 2016 Time-asymptotic stability of boundary-layers for a hyperbolic relaxation system. Zbl 0997.35007Liu, Hailiang; Yong, Wen-An 5 2001 Alternating evolution schemes for hyperbolic conservation laws. Zbl 1248.65092Saran, Haseena; Liu, Hailiang 5 2011 Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang 5 2015 Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105Lee, Yongki; Liu, Hailiang 5 2013 Semi-active fuzzy sliding mode control of full vehicle and suspensions. Zbl 1182.70067Liu, H.; Nonami, K.; Hagiwara, T. 5 2005 Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. Zbl 1473.65102Feng, Xiaobing; Liu, Hailiang; Ma, Shu 5 2019 Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M. 4 2014 Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428Li, Tong; Liu, Hailiang 4 2009 On a non-local selection-mutation model with a gradient flow structure. Zbl 1382.35313Jabin, Pierre-Emmanuel; Liu, Hailiang 4 2017 Nonlinear stability and existence of stationary discrete travelling waves for the relaxing schemes. Zbl 0934.65101Liu, Hailiang; Wang, Jinghua; Yang, Tong 4 1999 Long-time diffusive behavior of solutions to a hyperbolic relaxation system. Zbl 0981.35035Liu, Hailiang; Natalini, Roberto 4 2001 Critical thresholds in the semiclassical limit of 2D rotational Schrödinger equations. Zbl 1089.35052Liu, Hailiang 4 2006 On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations. Zbl 1461.65241Liu, Hailiang; Huang, Yunqing; Lu, Wenying; Yi, Nianyu 4 2019 A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364Yi, Nianyu; Huang, Yunqing; Liu, Hailiang 4 2019 Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386Qin, Yuming; Liu, Hailiang; Song, Changming 4 2008 Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity. Zbl 1452.65260Yu, Hui; Liu, Hailiang 4 2019 Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system. Zbl 1473.65263Liu, Hailiang; Maimaitiyiming, Wumaier 4 2020 On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190Ha, Tae Gab; Liu, Hailiang 3 2015 Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations. Zbl 1376.65122Liu, Hailiang; Wen, Hairui 3 2018 A uniform multiscale method for 2D static and dynamic analyses of heterogeneous materials. Zbl 1352.74459Zhang, H. W.; Liu, H.; Wu, J. K. 3 2013 Computation of free surface waves around an arbitrary body by a Navier- Stokes solver using the pseudocompressibility technique. Zbl 0814.76066Liu, H.; Ikehata, M. 3 1994 High order unconditionally energy stable RKDG schemes for the Swift-Hohenberg equation. Zbl 1491.65145Liu, Hailiang; Yin, Peimeng 3 2022 Positivity-preserving third order DG schemes for Poisson-Nernst-Planck equations. Zbl 07517725Liu, Hailiang; Wang, Zhongming; Yin, Peimeng; Yu, Hui 1 2022 Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 1471.35277Liu, Hailiang; Maimaitiyiming, Wumaier 8 2021 An energy stable and positivity-preserving scheme for the Maxwell-Stefan diffusion system. Zbl 07410698Huo, Xiaokai; Liu, Hailiang; Tzavaras, Athanasios E.; Wang, Shuaikun 2 2021 Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations. Zbl 1465.65100Liu, Hailiang 1 2021 Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation. Zbl 1480.65264Liu, Hailiang; Yin, Peimeng 1 2021 Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145Bhatnagar, Manas; Liu, Hailiang 6 2020 Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system. Zbl 1473.65263Liu, Hailiang; Maimaitiyiming, Wumaier 4 2020 Positive and free energy satisfying schemes for diffusion with interaction potentials. Zbl 07507217Liu, Hailiang; Maimaitiyiming, Wumaier 1 2020 Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372Liu, Hailiang; Yin, Peimeng 14 2019 Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. Zbl 1473.65102Feng, Xiaobing; Liu, Hailiang; Ma, Shu 5 2019 On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations. Zbl 1461.65241Liu, Hailiang; Huang, Yunqing; Lu, Wenying; Yi, Nianyu 4 2019 A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364Yi, Nianyu; Huang, Yunqing; Liu, Hailiang 4 2019 Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity. Zbl 1452.65260Yu, Hui; Liu, Hailiang 4 2019 A high order positivity preserving DG method for coagulation-fragmentation equations. Zbl 1426.65146Liu, Hailiang; Gröpler, Robin; Warnecke, Gerald 3 2019 An invariant-region-preserving limiter for DG schemes to isentropic Euler equations. Zbl 1416.76153Jiang, Yi; Liu, Hailiang 3 2019 Time-asymptotic convergence rates towards discrete steady states of a nonlocal selection-mutation model. Zbl 1427.35292Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang 2 2019 A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168Liu, Hailiang; Yin, Peimeng 10 2018 Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations. Zbl 1416.65293Jiang, Yi; Liu, Hailiang 9 2018 Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations. Zbl 1376.65122Liu, Hailiang; Wen, Hairui 3 2018 An invariant-region-preserving (IRP) limiter to DG methods for compressible Euler equations. Zbl 1407.65191Jiang, Yi; Liu, Hailiang 2 2018 Error estimates of the third order Runge-Kutta alternating evolution discontinuous Galerkin method for convection-diffusion problems. Zbl 1422.65261Liu, Hailiang; Wen, Hairui 1 2018 Error estimates for the iterative discontinuous Galerkin method to the nonlinear Poisson-Boltzmann equation. Zbl 1488.65669Yin, Peimeng; Huang, Yunqing; Liu, Hailiang 1 2018 A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021Liu, Hailiang; Wang, Zhongming 25 2017 Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin 24 2017 Tiling sets and spectral sets over finite fields. Zbl 1376.52038Aten, C.; Ayachi, B.; Bau, E.; FitzPatrick, D.; Iosevich, A.; Liu, H.; Lott, A.; MacKinnon, I.; Maimon, S.; Nan, S.; Pakianathan, J.; Petridis, G.; Rojas Mena, C.; Sheikh, A.; Tribone, T.; Weill, J.; Yu, C. 7 2017 On a non-local selection-mutation model with a gradient flow structure. Zbl 1382.35313Jabin, Pierre-Emmanuel; Liu, Hailiang 4 2017 A finite volume method for nonlocal competition-mutation equations with a gradient flow structure. Zbl 1378.92047Cai, Wenli; Liu, Hailiang 2 2017 Error estimates for Gaussian beam methods applied to symmetric strictly hyperbolic systems. Zbl 07213155Liu, Hailiang; Pryporov, Maksym 1 2017 A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462Liu, Hailiang; Yi, Nianyu 20 2016 An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158Liu, Hailiang; Wang, Zhongming 14 2016 An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321Liu, Hailiang; Xing, Yulong 10 2016 On invariant-preserving finite difference schemes for the Camassa-Holm equation and the two-component Camassa-Holm system. Zbl 1388.65059Liu, Hailiang; Pendleton, Terrance 6 2016 Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356Liu, Hailiang; Pollack, Michael 5 2016 Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation. Zbl 1362.37161Levermore, C. David; Liu, Hailiang; Pego, Robert L. 5 2016 Sobolev and max norm error estimates for Gaussian beam superpositions. Zbl 1372.35263Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M. 2 2016 Oscillatory traveling wave solutions to an attractive chemotaxis system. Zbl 1350.35055Li, Tong; Liu, Hailiang; Wang, Lihe 1 2016 Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141Liu, Hailiang 31 2015 Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358Lu, Wenying; Huang, Yunqing; Liu, Hailiang 20 2015 A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177Liu, Hailiang; Ploymaklam, Nattapol 19 2015 The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143Liu, Hailiang; Yu, Hui 17 2015 Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420Lee, Yongki; Liu, Hailiang 12 2015 Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250Lee, Yongki; Liu, Hailiang 5 2015 Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang 5 2015 On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190Ha, Tae Gab; Liu, Hailiang 3 2015 Entropy satisfying schemes for computing selection dynamics in competitive interactions. Zbl 1318.65085Liu, Hailiang; Cai, Wenli; Su, Ning 3 2015 Error estimates of the Bloch band-based Gaussian beam superposition for the Schrödinger equation. Zbl 1348.35213Liu, Hailiang; Pryporov, Maksym 2 2015 A free energy satisfying finite difference method for Poisson-Nernst-Planck equations. Zbl 1349.65317Liu, Hailiang; Wang, Zhongming 38 2014 Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038Liu, Hailiang; Yu, Hui 18 2014 Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461Liu, Hailiang; Pollack, Michael 7 2014 A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158Huang, Yunqing; Liu, Hailiang; Yi, Nianyu 6 2014 An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162Yin, Peimeng; Huang, Yunqing; Liu, Hailiang 6 2014 Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M. 4 2014 Entropy/energy stable schemes for evolutionary dispersal models. Zbl 1349.65318Liu, Hailiang; Yu, Hui 1 2014 A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect. Zbl 1297.65122Yi, Nianyu; Huang, Yunqing; Liu, Hailiang 29 2013 Error estimates for Gaussian beam superpositions. Zbl 1277.35236Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M. 23 2013 Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105Lee, Yongki; Liu, Hailiang 5 2013 A uniform multiscale method for 2D static and dynamic analyses of heterogeneous materials. Zbl 1352.74459Zhang, H. W.; Liu, H.; Wu, J. K. 3 2013 Alternating evolution schemes for Hamilton-Jacobi equations. Zbl 1270.65049Liu, Hailiang; Pollack, Michael; Saran, Haseena 2 2013 Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009Huang, Yunqing; Liu, Hailiang; Yi, Nianyu 12 2012 Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. Zbl 1395.76047Degond, P.; Liu, H.; Savelief, D.; Vignal, M.-H. 10 2012 An entropy satisfying conservative method for the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model. Zbl 1422.74097Liu, Hailiang; Yu, Hui 10 2012 Global well-posedness for the microscopic FENE model with a sharp boundary condition. Zbl 1233.35109Liu, Hailiang; Shin, Jaemin 6 2012 The Cauchy-Dirichlet problem for the finitely extensible nonlinear elastic dumbbell model of polymeric fluids. Zbl 1257.35144Liu, Hailiang; Shin, Jaemin 2 2012 Alternating evolution schemes for hyperbolic conservation laws. Zbl 1248.65092Saran, Haseena; Liu, Hailiang 5 2011 A level set approach for dilute non-collisional fluid-particle flows. Zbl 1391.76348Liu, Hailiang; Wang, Zhongming; Fox, Rodney O. 1 2011 The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200Liu, Hailiang; Yan, Jue 72 2010 Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031Liu, Hailiang; Ralston, James 12 2010 Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284Liu, Hailiang; Ralston, James 8 2010 Global regularity of the 4D restricted Euler equations. Zbl 1193.37123Liu, Hailiang; Tadmor, Eitan; Wei, Dongming 7 2010 Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175Liu, Hailiang; Yin, Zhaoyang 6 2010 The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227Liu, Hailiang; Yan, Jue 93 2009 Kinetic models for polymers with inertial effects. Zbl 1183.76614Degond, Pierre; Liu, Hailiang 12 2009 Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062Li, Tong; Liu, Hailiang 11 2009 Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428Li, Tong; Liu, Hailiang 4 2009 Development of an analytical \(\beta\)-function PDF integration algorithm for simulation of non-premixed turbulent combustion. Zbl 1405.80011Lien, F. S.; Liu, H.; Chui, E.; McCartney, C. J. 1 2009 On discreteness of the Hopf equation. Zbl 1149.65071Liu, Hai-liang 10 2008 Robust control of robotic manipulators based on integral sliding mode. Zbl 1154.93344Shi, J.; Liu, H.; Bajcinca, N. 6 2008 Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006Li, Tong; Liu, Hailiang 6 2008 A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063di Francesco, Marco; Fellner, Klemens; Liu, Hailiang 6 2008 Boundary conditions for the microscopic FENE models. Zbl 1147.76003Liu, Chun; Liu, Hailiang 5 2008 Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141Liu, Hailiang; Wang, Zhongming 5 2008 Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386Qin, Yuming; Liu, Hailiang; Song, Changming 4 2008 An alternating evolution approximation to systems of hyperbolic conservation laws. Zbl 1162.35049Liu, Hailiang 3 2008 Rigorous derivation of the hydrodynamical equations for rotating superfluids. Zbl 1144.81462Liu, Hailiang; Sparber, Christof 2 2008 A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations. Zbl 1168.65056Liu, Hailiang; Wang, Zhongming 1 2008 A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations. Zbl 1140.81399Liu, Hailiang; Wang, Zhongming 5 2007 Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101Liu, Hailiang 5 2007 Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations. Zbl 1146.78012Liu, Hailiang; Wang, Zhongming 5 2007 The modular multisensory DLR-HIT-Hand. Zbl 1183.70026Liu, H.; Meusel, P.; Seitz, N.; Willberg, B.; Hirzinger, G.; Jin, M. H.; Liu, Y. W.; Wei, R.; Xie, Z. W. 1 2007 A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. Zbl 1092.65083Liu, Hailiang; Yan, Jue 32 2006 Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069Liu, Hailiang 23 2006 Multi-valued solution and level set methods in computational high frequency wave propagation. Zbl 1120.65110Liu, H.; Osher, S.; Tsai, R. 13 2006 A level set framework for capturing multi-valued solutions of nonlinear first-order equations. Zbl 1109.65080Liu, Hailiang; Cheng, Li-Tien; Osher, Stanley 7 2006 Critical thresholds in the semiclassical limit of 2D rotational Schrödinger equations. Zbl 1089.35052Liu, Hailiang 4 2006 Sharp interface Cartesian grid method. I: An easily implemented technique for 3D moving boundary computations. Zbl 1154.76359Marella, S.; Krishnan, S.; Liu, H.; Udaykumar, H. S. 75 2005 Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation. Zbl 1072.65132Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Yen-Hsi Richard 35 2005 Sharp interface Cartesian grid method. II: A technique for simulating droplet interactions with surfaces of arbitrary shape. Zbl 1154.76358Liu, H.; Krishnan, S.; Marella, S.; Udaykumar, H. S. 35 2005 Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential. Zbl 1092.76007Liu, Hailiang; Zhang, Hui; Zhang, Pingwen 31 2005 Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems. Zbl 1098.65094Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Richard 20 2005 ...and 47 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,106 Authors 78 Liu, Hailiang 22 Shen, Chun 22 Yang, Hanchun 20 Sun, Meina 19 Zhang, Yu 18 Shu, Chi-Wang 16 Huang, Yunqing 15 Cheng, Hongjun 15 Yi, Nianyu 13 Liu, Tiegang 12 Jin, Shi 12 Shao, Zhiqiang 12 Yin, Gan 12 Zhang, Yanyan 11 Wang, Jinhuan 11 Wang, Zhongming 11 Yan, Jue 9 Cheng, Jian 9 Guo, Lihui 9 Pang, Yicheng 9 Tadmor, Eitan 9 Xu, Yan 9 Yu, Xijun 9 Zhang, Pingwen 8 Huang, Chaobao 8 Li, Tong 8 Rozanova, Olga S. 8 Tan, Changhui 7 An, Na 7 Cheng, Yingda 7 Choi, Young-Pil 7 Degond, Pierre 7 Lee, Yongki 7 Meng, Xiong 7 Nedeljkov, Marko 7 Runborg, Olof 7 Sheng, Wancheng 7 Yin, Peimeng 6 Baccouch, Mahboub 6 Carrillo de la Plata, José Antonio 6 Fox, Rodney O. 6 Kim, Junseok 6 Mitrovic, Darko 6 Osher, Stanley Joel 6 Sarrico, Carlos Orlando R. 6 Titi, Edriss Saleh 6 Wang, Wei 6 Wu, Boying 6 Xia, Yinhua 6 Xing, Yulong 6 Yang, Xu 6 Zhou, Shenggao 6 Zhu, Changjiang 5 Cheng, Yao 5 Liu, Jinjing 5 Liu, Yong 5 Luo, Hong 5 Qian, Jianliang 5 Qu, Aifang 5 Süli, Endre E. 5 Tao, Qi 5 Tsai, Yen-Hsi Richard 5 Wen, Xin 5 Yan, Jinliang 5 Yong, Wen-An 5 Yuan, Hairong 5 Zhang, Fan 5 Zhang, Mengping 5 Zhang, Rongpei 5 Zhang, Zhiyue 5 Zhou, Zhennan 4 Barrett, John William 4 Bhatnagar, Manas 4 Dai, Limei 4 Dehghan Takht Fooladi, Mehdi 4 Du, Qiang 4 Gosse, Laurent 4 He, Dongdong 4 Kwon, Bongsuk 4 Lu, Benzhuo 4 Motamed, Mohammad 4 Nishikawa, Hiroaki 4 Pan, Kejia 4 Pu, Xueke 4 Ruan, Lizhi 4 Sheng, Shouqiong 4 Shu, Shi 4 Sun, Zhengjie 4 Xu, Jie 4 Yang, Junxiang 4 Yang, Ying 4 Yu, Hui 4 Yue, Huiqiang 4 Yuen, Manwai 4 Zhang, Dazhi 4 Zhang, Qiang 4 Zhang, Qingling 4 Zhang, Zhifei 4 Zhou, Hong 4 Zhu, Jiang ...and 1,006 more Authors all top 5 Cited in 162 Serials 97 Journal of Computational Physics 55 Journal of Scientific Computing 53 Journal of Differential Equations 34 Journal of Mathematical Analysis and Applications 25 Journal of Mathematical Physics 24 Journal of Computational and Applied Mathematics 21 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 21 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 21 Communications in Computational Physics 18 Physica D 16 Mathematics of Computation 15 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 Computers & Mathematics with Applications 14 Applied Numerical Mathematics 13 SIAM Journal on Numerical Analysis 13 Communications on Pure and Applied Analysis 12 Archive for Rational Mechanics and Analysis 12 Computers and Fluids 12 Applied Mathematics and Computation 12 SIAM Journal on Scientific Computing 12 Journal of Hyperbolic Differential Equations 11 Numerische Mathematik 11 Applied Mathematics Letters 10 SIAM Journal on Mathematical Analysis 9 Acta Applicandae Mathematicae 9 Numerical Algorithms 9 Nonlinear Analysis. 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Mathematics 4 Monatshefte für Mathematik 4 Applied Mathematical Modelling 4 Physics of Fluids 4 Nonlinear Dynamics 4 Journal of Mathematical Fluid Mechanics 4 European Journal of Mechanics. B. Fluids 4 Kinetic and Related Models 4 Journal of Applied Analysis and Computation 4 Open Mathematics 3 Journal of Statistical Physics 3 Nonlinearity 3 Advances in Mathematics 3 Numerical Methods for Partial Differential Equations 3 Communications in Partial Differential Equations 3 International Journal of Computer Mathematics 3 Mathematical Problems in Engineering 3 Mathematics and Mechanics of Solids 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 Journal of Nonlinear Mathematical Physics 3 Multiscale Modeling & Simulation 2 Rocky Mountain Journal of Mathematics 2 Bulletin of Mathematical Biology 2 Calcolo 2 Journal of Functional Analysis 2 Mathematics and Computers in Simulation 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Asymptotic Analysis 2 International Journal of Mathematics 2 Computational Mathematics and Mathematical Physics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Journal of Dynamics and Differential Equations 2 Applied and Computational Harmonic Analysis 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Discrete and Continuous Dynamical Systems. Series B 2 Computational Methods in Applied Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Thai Journal of Mathematics 2 Acta Numerica 2 International Journal of Numerical Analysis and Modeling 2 Discrete and Continuous Dynamical Systems. Series S 2 Research in the Mathematical Sciences 2 International Journal of Applied and Computational Mathematics 1 International Journal of General Systems 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Engineering Mathematics 1 Journal of Mathematical Biology 1 Moscow University Mathematics Bulletin 1 Physica A 1 Physics Letters. A 1 Theoretical and Mathematical Physics 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki ...and 62 more Serials all top 5 Cited in 33 Fields 689 Partial differential equations (35-XX) 408 Numerical analysis (65-XX) 329 Fluid mechanics (76-XX) 89 Statistical mechanics, structure of matter (82-XX) 46 Biology and other natural sciences (92-XX) 33 Optics, electromagnetic theory (78-XX) 24 Mechanics of deformable solids (74-XX) 23 Quantum theory (81-XX) 21 Dynamical systems and ergodic theory (37-XX) 18 Operations research, mathematical programming (90-XX) 14 Ordinary differential equations (34-XX) 14 Functional analysis (46-XX) 12 Geophysics (86-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 10 Relativity and gravitational theory (83-XX) 8 Probability theory and stochastic processes (60-XX) 8 Astronomy and astrophysics (85-XX) 7 Integral equations (45-XX) 6 Approximations and expansions (41-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Real functions (26-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Computer science (68-XX) 3 Mechanics of particles and systems (70-XX) 3 Systems theory; control (93-XX) 2 Operator theory (47-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) Citations by Year