## Liu, Tai-Ping

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 Author ID: liu.tai-ping Published as: Liu, Tai-Ping; Liu, Taiping; Liu, T.-P.; Liu, T. P.; Lin, Tai-Ping more...less Homepage: https://mathematics.stanford.edu/people/tai-ping-liu External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 166 Publications since 1974, including 6 Books 5 Contributions as Editor · 2 Further Contributions Reviewing Activity: 11 Reviews Biographic References: 5 Publications Co-Authors: 60 Co-Authors with 105 Joint Publications 1,756 Co-Co-Authors
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### Co-Authors

 66 single-authored 29 Yu, Shih-Hsien 18 Yang, Tong 7 Zeng, Yanni 5 Xin, Zhouping 3 Chen, I-Kun 3 Chern, I-Liang 3 Elling, Volker W. 3 Kuo, Hung-Wen 2 Caflisch, Russel E. 2 Chen, Chiun-Chuan 2 Chen, Gui-Qiang G. 2 Dafermos, Constantin 2 Frid, Hermano 2 Hoff, David 2 Hsiao, Ling 2 Hsu, Szebi 2 Linares, Felipe 2 Nishihara, Kenji 2 Noh, Se Eun 2 Ponce, Gustavo 2 Smoller, Joel Alan 2 Takata, Shigeru 2 Tsai, Li-cheng 2 Zumbrun, Kevin R. 1 Antman, Stuart S. 1 Bressan, Alberto 1 Chang, Sun-Yung Alice 1 Chorin, Alexandre Joel 1 Conlon, Joseph G. 1 Deng, Yinbin 1 Ding, Xia-xi 1 Freistühler, Heinrich 1 Funagane, Hitoshi 1 Fusco, Nicola 1 Glaz, Harland M. 1 Huang, Luping 1 Jiang, Jin-Cheng 1 Kawashima, Shuichi 1 Lan, Chiuya 1 Lee, Ming-Yi 1 LeFloch, Philippe Gerard 1 Levermore, C. David 1 Li, Caizhong 1 Li, Dening 1 Lien, Wen-Ching 1 Lin, Hueyer 1 Liu, Fonche 1 Matsumura, Akitaka 1 McIntosh, Alan 1 Nikkuni, Yoshiko 1 Nishibata, Shinya 1 Pierre, Michel 1 Ruggeri, Tommaso 1 Sone, Yoshio 1 Tan, Dechun 1 Teng, Zhen-Huan 1 Wang, Chinghua 1 Wang, Haitao 1 Wang, Weike 1 Yao, Zhengan 1 Ying, Longan 1 Zhao, Huijiang 1 Zheng, Yongshu
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### Serials

 23 Communications in Mathematical Physics 17 Communications on Pure and Applied Mathematics 14 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 11 Archive for Rational Mechanics and Analysis 11 Journal of Differential Equations 5 Indiana University Mathematics Journal 4 Memoirs of the American Mathematical Society 4 SIAM Journal on Mathematical Analysis 4 Methods and Applications of Analysis 3 Advances in Applied Mathematics 3 Discrete and Continuous Dynamical Systems 3 Journal of Hyperbolic Differential Equations 2 Journal of Mathematical Analysis and Applications 2 Transactions of the American Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 2 Bulletin of the Brazilian Mathematical Society. New Series 1 Journal of Mathematical Physics 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Chinese Annals of Mathematics. Series B 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of the American Mathematical Society 1 Forum Mathematicum 1 Japan Journal of Industrial and Applied Mathematics 1 Bulletin of the Institute of Mathematics. Academia Sinica 1 SIAM Journal on Applied Mathematics 1 Computers and Mathematics with Applications. Part A 1 Journal of Partial Differential Equations 1 Taiwanese Journal of Mathematics 1 The Asian Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Foundations of Computational Mathematics 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Analysis and Applications (Singapore) 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Graduate Studies in Mathematics 1 AMS/IP Studies in Advanced Mathematics 1 Kinetic and Related Models 1 Annals of Applied Mathematics
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### Fields

 150 Partial differential equations (35-XX) 99 Fluid mechanics (76-XX) 13 Statistical mechanics, structure of matter (82-XX) 8 Mechanics of deformable solids (74-XX) 6 Numerical analysis (65-XX) 5 General and overarching topics; collections (00-XX) 5 Classical thermodynamics, heat transfer (80-XX) 3 History and biography (01-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Ordinary differential equations (34-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Astronomy and astrophysics (85-XX)

### Citations contained in zbMATH Open

131 Publications have been cited 4,307 times in 2,400 Documents Cited by Year
Hyperbolic conservation laws with stiff relaxation terms and entropy. Zbl 0806.35112
Chen, Gui-Qiang; Levermore, C. David; Liu, Tai-Ping
1994
Hyperbolic conservation laws with relaxation. Zbl 0633.35049
Liu, Tai-Ping
1987
Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping. Zbl 0763.35058
Hsiao, Ling; Liu, Tai-Ping
1992
Boltzmann equation: micro-macro decompositions and positivity of shock profiles. Zbl 1092.82034
Liu, Tai-Ping; Yu, Shih-Hsien
2004
Vacuum states for compressible flow. Zbl 0970.76084
Liu, Tai-Ping; Xin, Zhouping; Yang, Tong
1998
The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimensions. Zbl 0912.35122
Liu, Tai-Ping; Wang, Weike
1998
Energy method for Boltzmann equation. Zbl 1098.82618
Liu, Tai-Ping; Yang, Tong; Yu, Shih-Hsien
2004
The Riemann problem for general systems of conservation laws. Zbl 0297.76057
Liu, Tai-Ping
1975
Nonlinear stability of rarefaction waves for compressible Navier-Stokes equations. Zbl 0682.35087
Liu, Tai-Ping; Xin, Zhouping
1988
Quasilinear hyperbolic systems. Zbl 0435.35054
Liu, Tai-Ping
1979
On the vacuum state for the isentropic gas dynamics equations. Zbl 0461.76055
Liu, T.-P.; Smoller, J. A.
1980
Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations. Zbl 0379.35048
Liu, Tai-Ping
1979
The Riemann problem for general $$2 \times 2$$ conservation laws. Zbl 0289.35063
Liu, Tai-Ping
1974
Compressible flow with damping and vacuum. Zbl 0865.35107
Liu, Tai-Ping
1996
Nonlinear stability of shock waves for viscous conservation laws. Zbl 0617.35058
Liu, Tai-Ping
1985
Pointwise convergence to shock waves for viscous conservation laws. Zbl 0902.35069
Liu, Tai-Ping
1997
The Green’s function and large-time behavior of solutions for the one-dimensional Boltzmann equation. Zbl 1111.76047
Liu, Tai-Ping; Yu, Shih-Hsien
2004
Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws. Zbl 0884.35073
Liu, Tai-Ping; Zeng, Yanni
1997
The deterministic version of the Glimm scheme. Zbl 0376.35042
Liu, Tai-Ping
1977
Source-solutions and asymptotic behavior in conservation laws. Zbl 0545.35057
Liu, Tai-Ping; Pierre, Michel
1984
$$L^1$$ stability estimates for $$n\times n$$ conservation laws. Zbl 0938.35093
Bressan, Alberto; Liu, Tai-Ping; Yang, Tong
1999
Zero relaxation and dissipation limits for hyperbolic conservation laws. Zbl 0797.35113
Chen, Gui-Qiang; Liu, Tai-Ping
1993
Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves. Zbl 0916.35103
Liu, Tai-Ping; Matsumura, Akitaka; Nishihara, Kenji
1998
Compressible Euler equations with vacuum. Zbl 0890.35111
Liu, Tai-Ping; Yang, Tong
1997
Admissible solutions of hyperbolic conservation laws. Zbl 0446.76058
Liu, Tai-Ping
1981
Solutions of Euler-Poisson equations for gaseous stars. Zbl 1038.76036
Deng, Yinbin; Liu, Tai-Ping; Yang, Tong; Yao, Zhengan
2002
The inviscid limit for the Navier-Stokes equations of compressible, isentropic flow with shock data. Zbl 0674.76047
Hoff, David; Liu, Tai-Ping
1989
Nonlinear stability and instability of transonic flows through a nozzle. Zbl 0576.76053
Liu, T. P.
1982
Supersonic flow onto a solid wedge. Zbl 1143.76030
Elling, Volker; Liu, Tai-Ping
2008
Linear and nonlinear large-time behavior of solutions of general systems of hyperbolic conservation laws. Zbl 0358.35014
Liu, Tai-Ping
1977
Nonlinear stability of rarefaction waves for the Boltzmann equation. Zbl 1095.76024
Liu, Tai-Ping; Yang, Tong; Yu, Shih-Hsien; Zhao, Hui-Jiang
2006
Nonlinear diffusive phenomena of nonlinear hyperbolic systems. Zbl 0804.35072
Hsiao, Ling; Liu, Taiping
1993
The entropy condition and the admissibility of shocks. Zbl 0332.76051
Liu, Tai-Ping
1976
Compressible flow with vacuum and physical singularity. Zbl 1033.76050
Liu, Tai-Ping; Yang, Tong
2000
Nonlinear stability of shock waves for viscous conservation laws. Zbl 0576.35077
Liu, Taiping
1985
Shock waves for compressible Navier-Stokes equations are stable. Zbl 0617.76069
Liu, Taiping
1986
Nonlinear resonance for quasilinear hyperbolic equation. Zbl 0662.35068
Liu, Tai-Ping
1987
Pointwise decay to contact discontinuities for systems of viscous conservation laws. Zbl 0928.35095
Liu, Tai-Ping; Xin, Zhouping
1997
Existence theory for nonlinear hyperbolic systems in nonconservative form. Zbl 0804.35086
Le Floch, Philippe; Liu, Tai-Ping
1993
Well-posedness theory for hyperbolic conservation laws. Zbl 1034.35073
Liu, Tai-Ping; Yang, Tong
1999
Asymptotic behavior for scalar viscous conservation laws with boundary effect. Zbl 0871.35050
Liu, Tai-Ping; Nishihara, Kenji
1997
Large-time behavior of solutions of initial and initial-boundary value problems of a general system of hyperbolic conservation laws. Zbl 0353.35009
Liu, Tai-Ping
1977
Solutions in the large for the equations of nonisentropic gas dynamics. Zbl 0361.35056
Liu, Tai-Ping
1977
Transonic gas flow in a duct of varying area. Zbl 0503.76076
Liu, Tai-Ping
1982
Initial-boundary value problems for gas dynamics. Zbl 0357.35016
Liu, Tai-Ping
1977
Nonlinear stability of a self-similar 3-dimensional gas flow. Zbl 0945.76033
Lien, Wen-Ching; Liu, Tai-Ping
1999
Compressible Navier-Stokes equations with zero heat conductivity. Zbl 0922.35117
Liu, Tai-Ping; Zeng, Yanni
1999
Green’s function of Boltzmann equation, 3-D waves. Zbl 1096.76051
Liu, Taiping; Yu, Shih-Hsien
2006
Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws. Zbl 0357.35059
Liu, Tai-Ping
1977
Convergence to diffusion waves of solutions for viscous conservation laws. Zbl 0635.76071
Chern, I.-Liang; Liu, Tai-Ping
1987
Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation. Zbl 1154.35015
Liu, Tai-Ping; Yu, Shih-Hsien
2007
The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow. Zbl 0598.76065
Glaz, Harland M.; Liu, Tai-Ping
1984
Propagation of a stationary shock layer in the presence of a boundary. Zbl 0895.76039
Liu, Tai-Ping; Yu, Shih-Hsien
1997
Riemann problems for reacting gas, with applications to transition. Zbl 0502.76088
Teng, Zhen-Huan; Chorin, Alexandre Joel; Liu, Tai-Ping
1982
Shock waves in conservation laws with physical viscosity. Zbl 1338.35369
Liu, Tai-Ping; Zeng, Yanni
2015
Time-asymptotic behavior of wave propagation around a viscous shock profile. Zbl 1190.35033
Liu, Tai-Ping; Zeng, Yanni
2009
Invariant manifolds for steady Boltzmann flows and applications. Zbl 1290.35181
Liu, Tai-Ping; Yu, Shih-Hsien
2013
$$L_1$$ stability for $$2\times 2$$ systems of hyperbolic conservation laws. Zbl 0924.35083
Liu, Tai-Ping; Yang, Tong
1999
The ellipticity principle for self-similar potential flows. Zbl 1089.35049
Elling, Volker; Liu, Tai-Ping
2005
Weak solutions of general systems of hyperbolic conservation laws. Zbl 1041.35038
Liu, Tai-Ping; Yang, Tong
2002
Large-time behavior of solutions to hyperbolic-elliptic coupled systems. Zbl 1073.35039
Kawashima, Shuichi; Nikkuni, Yoshiko; Nishibata, Shinya
2003
On a nonstrictly hyperbolic system of conservation laws. Zbl 0576.35075
Liu, Taiping; Wang, Chinghua
1985
Solving Boltzmann equation. I: Green’s function. Zbl 1432.35160
Liu, Tai-Ping; Yu, Shih-Hsien
2011
Thermal transpiration for the linearized Boltzmann equation. Zbl 1107.35004
Chen, Chiun-Chuan; Chen, I-Kun; Liu, Tai-Ping; Sone, Yoshio
2007
Nonlinear stability of an undercompressive shock for complex Burgers equation. Zbl 0821.35123
Liu, Tai-Ping; Zumbrun, Kevin
1995
Travelling waves in hyperelastic rods. Zbl 0408.73043
Antman, Stuart S.; Liu, Tai-Ping
1979
Existence of boundary layer solutions to the Boltzmann equation. Zbl 1172.35358
Chen, Chiun-Chuan; Liu, Tai-Ping; Yang, Tong
2004
On nonlinear stability of general undercompressive viscous shock waves. Zbl 0840.76028
Liu, Tai-Ping; Zumbrun, Kevin
1995
Invariants and asymptotic behavior of solutions of a conservation law. Zbl 0392.35041
Liu, Tai-Ping
1978
On boundary relation for some dissipative systems. Zbl 1273.35156
Liu, Tai-Ping; Yu, Shih-Hsien
2011
Nonlinear stability of overcompressive shock waves in a rotationally invariant system of viscous conservation laws. Zbl 0768.76024
Freistühler, Heinrich; Liu, Tai-Ping
1993
$$L_1$$ stability of conservation laws with coinciding Hugoniot and characteristic curves. Zbl 0935.35090
Liu, Tai-Ping; Yang, Tong
1999
A new entropy functional for a scalar conservation law. Zbl 0941.35051
Liu, Tai-Ping; Yang, Tong
1999
Uniqueness of weak solutions of the Cauchy problem for general 2 x 2 conservation laws. Zbl 0288.76031
Liu, Tai-Ping
1976
A scalar combustion model. Zbl 0734.76083
Liu, Tai-Ping; Zhang, Tong
1991
Nonlinear stability of strong detonations for a viscous combustion model. Zbl 0829.35053
Liu, Tai-Ping; Ying, Long-An
1995
Wave propagation for the compressible Navier-Stokes equations. Zbl 1327.76112
Liu, Tai-Ping; Noh, Se Eun
2015
Stability of shock waves for the Broadwell equations. Zbl 0665.76089
Caflisch, Russel E.; Liu, Tai-Ping
1988
Hyperbolic and viscous conservation laws. Zbl 0940.35004
Liu, Tai-Ping
2000
Existence and uniqueness theorems for Riemann problems. Zbl 0317.35062
Liu, Tai-Ping
1975
Boundary singularity for thermal transpiration problem of the linearized Boltzmann equation. Zbl 1293.35193
Chen, I-Kun; Liu, Tai-Ping; Takata, Shigeru
2014
The free piston problem for gas dynamics. Zbl 0398.76060
Liu, Tai-Ping
1978
Asymptotic behavior of solutions of general system of nonlinear hyperbolic conservation laws. Zbl 0373.35005
Liu, Tai-Ping
1978
Nonlinear stability of weak detonation waves for a combustion model. Zbl 0976.76036
Liu, Tai-Ping; Yu, Shih-Hsien
1999
Large-time behavior of solutions for the Boltzmann equation with hard potentials. Zbl 1190.82034
Lee, Ming-Yi; Liu, Tai-Ping; Yu, Shih-Hsien
2007
Free molecular flow with boundary effect. Zbl 1263.82043
Kuo, Hung-Wen; Liu, Tai-Ping; Tsai, Li-Cheng
2013
Stability of viscous shock waves associated with a system of nonstrictly hyperbolic conservation laws. Zbl 0789.35109
Liu, Tai-Ping; Xin, Zhouping
1992
Entropy production and admissibility of shocks. Zbl 1029.35172
Liu, Tai-Ping; Ruggeri, Tommaso
2003
Shock waves in the nonisentropic gas flow. Zbl 0331.35042
Liu, Tai-Ping
1976
Stability of strong detonation travelling waves to combustion model. Zbl 0862.35048
Li, Dening; Liu, Tai-Ping; Tan, Dechun
1996
Resonance for quasilinear hyperbolic equation. Zbl 0501.76048
Liu, Tai-Ping
1982
Continuum shock profiles for discrete conservation laws. I: Construction. Zbl 0933.35137
Liu, Tai-Ping; Yu, Shih-Hsien
1999
Exact solutions to supersonic flow onto a solid wedge. Zbl 1354.76084
Elling, V.; Liu, T.-P.
2008
A conservative, piecewise-steady difference scheme for transonic nozzle flow. Zbl 0589.76078
Huang, Luping; Liu, Tai-Ping
1986
Equilibrating effects of boundary and collision in rarefied gases. Zbl 1354.76158
Kuo, Hung-Wen; Liu, Tai-Ping; Tsai, Li-Cheng
2014
Admissibility criteria for hyperbolic conservation laws. Zbl 0444.58016
Conlon, Joseph G.; Liu, Tai-Ping
1981
Erratum: Convergence of diffusion waves of solutions for viscous conservation laws. Zbl 0662.76114
Chern, I.-Liang; Liu, Tai-Ping
1989
Interactions of nonlinear hyperbolic waves. Zbl 0820.35109
Liu, Tai-Ping
1991
Asymptotic states for hyperbolic conservation laws with a moving source. Zbl 0544.76059
Li, Caizhong; Liu, Taiping
1983
Viscous rarefaction waves. Zbl 1216.35120
Liu, Tai-Ping; Yu, Shih-Hsien
2010
Navier-Stokes equations in gas dynamics: Green’s function, singularity, and well-posedness. Zbl 07492700
Liu, Tai-Ping; Yu, Shih-Hsien
2022
Boltzmann collision operator for the infinite range potential: a limit problem. Zbl 1423.35292
Jiang, Jin-Cheng; Liu, Tai-Ping
2019
Multi-dimensional wave propagation over a Burgers shock profile. Zbl 1394.35364
Liu, Tai-Ping; Yu, Shih-Hsien
2018
Singularity of the velocity distribution function in molecular velocity space. Zbl 1335.35174
Chen, I-Kun; Funagane, Hitoshi; Liu, Tai-Ping; Takata, Shigeru
2016
Proceedings of the XV international conference on hyperbolic problems: theory, numerics, applications. Zbl 1354.00090
2016
Shock waves in conservation laws with physical viscosity. Zbl 1338.35369
Liu, Tai-Ping; Zeng, Yanni
2015
Wave propagation for the compressible Navier-Stokes equations. Zbl 1327.76112
Liu, Tai-Ping; Noh, Se Eun
2015
Boundary singularity for thermal transpiration problem of the linearized Boltzmann equation. Zbl 1293.35193
Chen, I-Kun; Liu, Tai-Ping; Takata, Shigeru
2014
Equilibrating effects of boundary and collision in rarefied gases. Zbl 1354.76158
Kuo, Hung-Wen; Liu, Tai-Ping; Tsai, Li-Cheng
2014
Boundary wave propagator for compressible Navier-Stokes equations. Zbl 1323.35132
Liu, Tai-Ping; Yu, Shih-Hsien
2014
Invariant manifolds for steady Boltzmann flows and applications. Zbl 1290.35181
Liu, Tai-Ping; Yu, Shih-Hsien
2013
Free molecular flow with boundary effect. Zbl 1263.82043
Kuo, Hung-Wen; Liu, Tai-Ping; Tsai, Li-Cheng
2013
Aspects of dissipation for compressible fluids and kinetic theory. Zbl 1292.35233
Liu, Tai-Ping
2013
Dirichlet-Neumann kernel for hyperolic-dissipative system in half-space. Zbl 1304.35410
Liu, Tai-Ping; Yu, Shih-Hsien
2012
Solving Boltzmann equation. I: Green’s function. Zbl 1432.35160
Liu, Tai-Ping; Yu, Shih-Hsien
2011
On boundary relation for some dissipative systems. Zbl 1273.35156
Liu, Tai-Ping; Yu, Shih-Hsien
2011
Multi-dimensional gas flow: some historical perspectives. Zbl 1278.35159
Liu, Tai-Ping
2011
Viscous rarefaction waves. Zbl 1216.35120
Liu, Tai-Ping; Yu, Shih-Hsien
2010
Mixture lemma. Zbl 1425.35132
Kuo, Hung-Wen; Liu, Tai-Ping; Noh, Se Eun
2010
Viscous conservation laws. I: Scalar laws. Zbl 1227.35006
Liu, Tai-Ping; Yu, Shih-Hsien; Zeng, Yanni
2010
Time-asymptotic behavior of wave propagation around a viscous shock profile. Zbl 1190.35033
Liu, Tai-Ping; Zeng, Yanni
2009
On Green’s function for hyperbolic-parabolic systems. Zbl 1212.35044
Liu, Taiping; Zeng, Yanni
2009
Boltzmann equation, boundary effects. Zbl 1160.76041
Liu, Tai-Ping; Yu, Shih-Hsien
2009
Viscous shock wave tracing, local conservation laws, and pointwise estimates. Zbl 1188.35118
Liu, Tai-Ping; Yu, Shih-Hsien
2009
Supersonic flow onto a solid wedge. Zbl 1143.76030
Elling, Volker; Liu, Tai-Ping
2008
Exact solutions to supersonic flow onto a solid wedge. Zbl 1354.76084
Elling, V.; Liu, T.-P.
2008
Diffusion under gravitational and boundary effects. Zbl 1388.76337
Liu, Tai-Ping; Yu, Shih-Hsien
2008
Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation. Zbl 1154.35015
Liu, Tai-Ping; Yu, Shih-Hsien
2007
Thermal transpiration for the linearized Boltzmann equation. Zbl 1107.35004
Chen, Chiun-Chuan; Chen, I-Kun; Liu, Tai-Ping; Sone, Yoshio
2007
Large-time behavior of solutions for the Boltzmann equation with hard potentials. Zbl 1190.82034
Lee, Ming-Yi; Liu, Tai-Ping; Yu, Shih-Hsien
2007
Nonlinear stability of rarefaction waves for the Boltzmann equation. Zbl 1095.76024
Liu, Tai-Ping; Yang, Tong; Yu, Shih-Hsien; Zhao, Hui-Jiang
2006
Green’s function of Boltzmann equation, 3-D waves. Zbl 1096.76051
Liu, Taiping; Yu, Shih-Hsien
2006
The ellipticity principle for self-similar potential flows. Zbl 1089.35049
Elling, Volker; Liu, Tai-Ping
2005
Boltzmann equation: micro-macro decompositions and positivity of shock profiles. Zbl 1092.82034
Liu, Tai-Ping; Yu, Shih-Hsien
2004
Energy method for Boltzmann equation. Zbl 1098.82618
Liu, Tai-Ping; Yang, Tong; Yu, Shih-Hsien
2004
The Green’s function and large-time behavior of solutions for the one-dimensional Boltzmann equation. Zbl 1111.76047
Liu, Tai-Ping; Yu, Shih-Hsien
2004
Existence of boundary layer solutions to the Boltzmann equation. Zbl 1172.35358
Chen, Chiun-Chuan; Liu, Tai-Ping; Yang, Tong
2004
Propagation of viscous shock waves away from the boundary. Zbl 1085.35102
Lan, Chiu-Ya; Lin, Huey-Er; Liu, Tai-Ping; Yu, Shih-Hsien
2004
Large-time behavior of solutions to hyperbolic-elliptic coupled systems. Zbl 1073.35039
Kawashima, Shuichi; Nikkuni, Yoshiko; Nishibata, Shinya
2003
Entropy production and admissibility of shocks. Zbl 1029.35172
Liu, Tai-Ping; Ruggeri, Tommaso
2003
Solutions of Euler-Poisson equations for gaseous stars. Zbl 1038.76036
Deng, Yinbin; Liu, Tai-Ping; Yang, Tong; Yao, Zhengan
2002
Weak solutions of general systems of hyperbolic conservation laws. Zbl 1041.35038
Liu, Tai-Ping; Yang, Tong
2002
Shock waves. Zbl 1136.35423
Liu, Tai-Ping
2002
Compressible flow with vacuum and physical singularity. Zbl 1033.76050
Liu, Tai-Ping; Yang, Tong
2000
Hyperbolic and viscous conservation laws. Zbl 0940.35004
Liu, Tai-Ping
2000
$$L^1$$ stability estimates for $$n\times n$$ conservation laws. Zbl 0938.35093
Bressan, Alberto; Liu, Tai-Ping; Yang, Tong
1999
Well-posedness theory for hyperbolic conservation laws. Zbl 1034.35073
Liu, Tai-Ping; Yang, Tong
1999
Nonlinear stability of a self-similar 3-dimensional gas flow. Zbl 0945.76033
Lien, Wen-Ching; Liu, Tai-Ping
1999
Compressible Navier-Stokes equations with zero heat conductivity. Zbl 0922.35117
Liu, Tai-Ping; Zeng, Yanni
1999
$$L_1$$ stability for $$2\times 2$$ systems of hyperbolic conservation laws. Zbl 0924.35083
Liu, Tai-Ping; Yang, Tong
1999
$$L_1$$ stability of conservation laws with coinciding Hugoniot and characteristic curves. Zbl 0935.35090
Liu, Tai-Ping; Yang, Tong
1999
A new entropy functional for a scalar conservation law. Zbl 0941.35051
Liu, Tai-Ping; Yang, Tong
1999
Nonlinear stability of weak detonation waves for a combustion model. Zbl 0976.76036
Liu, Tai-Ping; Yu, Shih-Hsien
1999
Continuum shock profiles for discrete conservation laws. I: Construction. Zbl 0933.35137
Liu, Tai-Ping; Yu, Shih-Hsien
1999
Continuum shock profiles for discrete conservation laws. II: Stability. Zbl 0965.35095
Liu, Tai-Ping; Yu, Shih-Hsien
1999
Vacuum states for compressible flow. Zbl 0970.76084
Liu, Tai-Ping; Xin, Zhouping; Yang, Tong
1998
The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimensions. Zbl 0912.35122
Liu, Tai-Ping; Wang, Weike
1998
Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves. Zbl 0916.35103
Liu, Tai-Ping; Matsumura, Akitaka; Nishihara, Kenji
1998
Pointwise convergence to shock waves for viscous conservation laws. Zbl 0902.35069
Liu, Tai-Ping
1997
Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws. Zbl 0884.35073
Liu, Tai-Ping; Zeng, Yanni
1997
Compressible Euler equations with vacuum. Zbl 0890.35111
Liu, Tai-Ping; Yang, Tong
1997
Pointwise decay to contact discontinuities for systems of viscous conservation laws. Zbl 0928.35095
Liu, Tai-Ping; Xin, Zhouping
1997
Asymptotic behavior for scalar viscous conservation laws with boundary effect. Zbl 0871.35050
Liu, Tai-Ping; Nishihara, Kenji
1997
Propagation of a stationary shock layer in the presence of a boundary. Zbl 0895.76039
Liu, Tai-Ping; Yu, Shih-Hsien
1997
Uniform $$L_1$$ boundedness of solutions of hyperbolic conservation laws. Zbl 0972.35069
Liu, Tai-Ping; Yang, Tong
1997
Nonlinear waves for viscous conservation laws. Zbl 0891.35093
Liu, Tai-Ping
1997
Compressible flow with damping and vacuum. Zbl 0865.35107
Liu, Tai-Ping
1996
Stability of strong detonation travelling waves to combustion model. Zbl 0862.35048
Li, Dening; Liu, Tai-Ping; Tan, Dechun
1996
Nonlinear hyperbolic-dissipative partial differential equations. Zbl 0868.35072
Liu, Tai-Ping
1996
Nonlinear stability of an undercompressive shock for complex Burgers equation. Zbl 0821.35123
Liu, Tai-Ping; Zumbrun, Kevin
1995
On nonlinear stability of general undercompressive viscous shock waves. Zbl 0840.76028
Liu, Tai-Ping; Zumbrun, Kevin
1995
Nonlinear stability of strong detonations for a viscous combustion model. Zbl 0829.35053
Liu, Tai-Ping; Ying, Long-An
1995
Hyperbolic conservation laws with stiff relaxation terms and entropy. Zbl 0806.35112
Chen, Gui-Qiang; Levermore, C. David; Liu, Tai-Ping
1994
Zero relaxation and dissipation limits for hyperbolic conservation laws. Zbl 0797.35113
Chen, Gui-Qiang; Liu, Tai-Ping
1993
Nonlinear diffusive phenomena of nonlinear hyperbolic systems. Zbl 0804.35072
Hsiao, Ling; Liu, Taiping
1993
Existence theory for nonlinear hyperbolic systems in nonconservative form. Zbl 0804.35086
Le Floch, Philippe; Liu, Tai-Ping
1993
Nonlinear stability of overcompressive shock waves in a rotationally invariant system of viscous conservation laws. Zbl 0768.76024
Freistühler, Heinrich; Liu, Tai-Ping
1993
Nonlinear stability and instability of overcompressive shock waves. Zbl 0788.76058
Liu, Tai-Ping
1993
Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping. Zbl 0763.35058
Hsiao, Ling; Liu, Tai-Ping
1992
Stability of viscous shock waves associated with a system of nonstrictly hyperbolic conservation laws. Zbl 0789.35109
Liu, Tai-Ping; Xin, Zhouping
1992
A scalar combustion model. Zbl 0734.76083
Liu, Tai-Ping; Zhang, Tong
1991
Interactions of nonlinear hyperbolic waves. Zbl 0820.35109
Liu, Tai-Ping
1991
Nonlinear hyperbolic-parabolic partial differential equations. Zbl 0819.35101
Liu, Tai-Ping
1991
On the viscosity criterion for hyperbolic conservation laws. Zbl 0729.76637
Liu, Tai-Ping
1991
Nonlinear singular Sturm-Liouville problems and an application to transonic flow through a nozzle. Zbl 0693.34016
Hsu, Sze-Bi; Liu, Tai-Ping
1990
Overcompressive shock waves. Zbl 0731.35063
Liu, Tai-Ping; Xin, Zhouping
1990
The inviscid limit for the Navier-Stokes equations of compressible, isentropic flow with shock data. Zbl 0674.76047
Hoff, David; Liu, Tai-Ping
1989
Erratum: Convergence of diffusion waves of solutions for viscous conservation laws. Zbl 0662.76114
Chern, I.-Liang; Liu, Tai-Ping
1989
Nonlinear stability of rarefaction waves for compressible Navier-Stokes equations. Zbl 0682.35087
Liu, Tai-Ping; Xin, Zhouping
1988
Stability of shock waves for the Broadwell equations. Zbl 0665.76089
Caflisch, Russel E.; Liu, Tai-Ping
1988
Nonlinear waves for viscoelasticity with fading memory. Zbl 0662.35004
Liu, Tai-Ping
1988
Hyperbolic conservation laws with relaxation. Zbl 0633.35049
Liu, Tai-Ping
1987
Nonlinear resonance for quasilinear hyperbolic equation. Zbl 0662.35068
Liu, Tai-Ping
1987
Convergence to diffusion waves of solutions for viscous conservation laws. Zbl 0635.76071
Chern, I.-Liang; Liu, Tai-Ping
1987
Pointwise convergence to N-waves for solutions of hyperbolic conservation laws. Zbl 0646.35053
Liu, Tai-Ping
1987
Shock waves for compressible Navier-Stokes equations are stable. Zbl 0617.76069
Liu, Taiping
1986
A conservative, piecewise-steady difference scheme for transonic nozzle flow. Zbl 0589.76078
Huang, Luping; Liu, Tai-Ping
1986
Nonlinear stability of shock waves for viscous conservation laws. Zbl 0617.35058
Liu, Tai-Ping
1985
Nonlinear stability of shock waves for viscous conservation laws. Zbl 0576.35077
Liu, Taiping
1985
On a nonstrictly hyperbolic system of conservation laws. Zbl 0576.35075
Liu, Taiping; Wang, Chinghua
1985
...and 31 more Documents
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### Cited by 1,711 Authors

 84 Yang, Tong 69 Zhu, Changjiang 60 Liu, Tai-Ping 54 Zhao, Huijiang 46 Chen, Gui-Qiang G. 46 Xin, Zhouping 45 Wang, Weike 37 Zumbrun, Kevin R. 36 Duan, Renjun 32 Huang, Feimin 29 LeFloch, Philippe Gerard 28 Li, Hailiang 23 Wang, Yi 21 Kawashima, Shuichi 21 Luo, Tao 21 Yu, Shih-Hsien 20 Pan, Ronghua 20 Tan, Zhong 20 Yin, Huicheng 19 Marchesin, Dan 19 Yu, Hongjun 18 Guo, Zhenhua 18 Mei, Ming 17 Colombo, Rinaldo M. 17 Li, Yachun 17 Liu, Shuangqian 17 Shao, Zhiqiang 16 Liu, Hailiang 16 Lu, Yunguang 16 Yang, Xiongfeng 16 Yao, Zhengan 16 Yong, Wen-An 15 Hsiao, Ling 15 Zeng, Yanni 15 Zhang, Yinghui 15 Zhu, Shengguo 14 Amadori, Debora 14 Dafermos, Constantine M. 14 Gosse, Laurent 14 Ha, Seung-Yeal 14 Jang, Juhi 14 Yao, Lei 13 Coquel, Frédéric 13 Feldman, Mikhail 13 Hong, John Meng-Kai 13 Li, Yeping 13 Nishihara, Kenji 13 Radkevich, Evgeniĭ Vladimirovich 13 Wu, Guochun 13 Yin, Haiyan 13 Zeng, Huihui 13 Zhang, Yongqian 12 Bressan, Alberto 12 Corli, Andrea 12 Deng, Shijin 12 Lai, Geng 12 Li, Tong 12 Matsumura, Akitaka 12 Natalini, Roberto 12 Ruan, Lizhi 12 Sheng, Wancheng 12 Ukai, Seiji 12 Wang, Wenjun 12 Wu, Zhigang 12 Yuen, Manwai 11 Berthon, Christophe 11 Hu, Yanbo 11 Jin, Shi 11 Kong, Dexing 11 Lian, Ruxu 11 Wang, Zhian 11 Wu, Kung-Chien 11 Xiang, Wei 11 Xu, Jiang 11 Zhang, Ting 10 Asakura, Fumioki 10 Bianchini, Stefano 10 Chen, Geng 10 Christoforou, Cleopatra C. 10 Freistühler, Heinrich 10 Geng, Shifeng 10 Kim, Eun Heui 10 Pareschi, Lorenzo 10 Sun, Meina 10 Vasseur, Alexis F. 9 Chen, Shuxing 9 Fang, Daoyuan 9 Hattori, Harumi 9 Jiu, Quansen 9 Liu, Hongxia 9 Mai Duc Thanh 9 Marcati, Pierangelo 9 Nishibata, Shinya 9 Peng, Yuejun 9 Risebro, Nils Henrik 9 Russo, Giovanni 9 Serre, Denis 9 Shen, Chun 9 Takata, Shigeru 9 Tzavaras, Athanasios E. ...and 1,611 more Authors
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### Cited in 234 Serials

 379 Journal of Differential Equations 158 Archive for Rational Mechanics and Analysis 155 Journal of Mathematical Analysis and Applications 78 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 77 Journal of Hyperbolic Differential Equations 69 Communications in Mathematical Physics 69 Journal of Computational Physics 60 SIAM Journal on Mathematical Analysis 56 ZAMP. Zeitschrift für angewandte Mathematik und Physik 54 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 51 Communications in Partial Differential Equations 49 Journal of Mathematical Physics 40 Nonlinear Analysis. Real World Applications 35 Quarterly of Applied Mathematics 29 Applicable Analysis 29 Journal of Statistical Physics 28 Mathematical Methods in the Applied Sciences 28 Mathematics of Computation 28 Transactions of the American Mathematical Society 23 Physica D 23 Acta Mathematicae Applicatae Sinica. English Series 23 Acta Mathematica Scientia. Series B. (English Edition) 22 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 22 Communications on Pure and Applied Analysis 21 Discrete and Continuous Dynamical Systems 21 Kinetic and Related Models 20 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 17 Communications on Pure and Applied Mathematics 17 Chinese Annals of Mathematics. Series B 17 Science China. Mathematics 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 15 Computers & Mathematics with Applications 15 Applied Mathematics and Computation 15 Applied Mathematics Letters 14 Journal of Functional Analysis 14 Japan Journal of Industrial and Applied Mathematics 14 Journal of Mathematical Sciences (New York) 13 Journal of Computational and Applied Mathematics 13 Acta Applicandae Mathematicae 13 Journal of Mathematical Fluid Mechanics 12 Nonlinearity 12 Proceedings of the American Mathematical Society 12 Bulletin of the Brazilian Mathematical Society. New Series 11 Computers and Fluids 11 Journal of Scientific Computing 11 Nonlinear Analysis. Theory, Methods & Applications 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 9 Advances in Mathematics 9 Acta Mathematica Sinica. English Series 8 Computer Methods in Applied Mechanics and Engineering 8 Journal of Fluid Mechanics 8 Discrete and Continuous Dynamical Systems. Series B 8 Analysis and Applications (Singapore) 8 Networks and Heterogeneous Media 7 Numerische Mathematik 7 Advances in Applied Mathematics 7 Applied Numerical Mathematics 7 SIAM Journal on Applied Mathematics 7 Journal of Dynamics and Differential Equations 7 Calculus of Variations and Partial Differential Equations 7 NoDEA. Nonlinear Differential Equations and Applications 7 Boundary Value Problems 6 Transport Theory and Statistical Physics 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 6 Osaka Journal of Mathematics 6 Ricerche di Matematica 6 SIAM Journal on Scientific Computing 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Communications in Computational Physics 5 Wave Motion 5 Inventiones Mathematicae 5 SIAM Journal on Numerical Analysis 5 Journal of the American Mathematical Society 5 Bulletin of the American Mathematical Society. New Series 5 Physics of Fluids 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 5 Journal of Evolution Equations 5 Advances in Mathematical Physics 4 Studies in Applied Mathematics 4 Mathematical and Computer Modelling 4 Applications of Mathematics 4 Applied Mathematical Modelling 4 Journal of Elasticity 4 Journal of Applied Mathematics 4 Discrete and Continuous Dynamical Systems. Series S 4 Annals of PDE 3 Archiv der Mathematik 3 BIT 3 Mathematische Annalen 3 Proceedings of the Japan Academy. Series A 3 Rendiconti del Seminario Matematico della Università di Padova 3 Science in China. Series A 3 Boletim da Sociedade Brasileira de Matemática. Nova Série 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Computational and Applied Mathematics 3 Bulletin des Sciences Mathématiques 3 Wuhan University Journal of Natural Sciences (WUJNS) 3 European Journal of Mechanics. B. Fluids 3 Computational Geosciences ...and 134 more Serials
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### Cited in 41 Fields

 2,073 Partial differential equations (35-XX) 1,269 Fluid mechanics (76-XX) 254 Numerical analysis (65-XX) 214 Statistical mechanics, structure of matter (82-XX) 110 Mechanics of deformable solids (74-XX) 74 Classical thermodynamics, heat transfer (80-XX) 43 Ordinary differential equations (34-XX) 42 Astronomy and astrophysics (85-XX) 38 Biology and other natural sciences (92-XX) 34 Optics, electromagnetic theory (78-XX) 29 Dynamical systems and ergodic theory (37-XX) 28 Operations research, mathematical programming (90-XX) 24 Integral equations (45-XX) 22 Relativity and gravitational theory (83-XX) 16 Operator theory (47-XX) 15 Global analysis, analysis on manifolds (58-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Probability theory and stochastic processes (60-XX) 11 Differential geometry (53-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 8 Functional analysis (46-XX) 8 Geophysics (86-XX) 7 Systems theory; control (93-XX) 6 Real functions (26-XX) 6 Mechanics of particles and systems (70-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Computer science (68-XX) 5 Quantum theory (81-XX) 4 Integral transforms, operational calculus (44-XX) 4 General topology (54-XX) 3 Combinatorics (05-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX)

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