Tai-Ping Liu

Q: What Schools Are Affiliated With Tai-Ping Liu

Tai-Ping Liu is affiliated with the following schools: Oregon State University, Chongqing University, California Institute of Technology, University of Michigan, Stanford University, National Taiwan University, New York University

Tai-Ping Liu's AcademicInfluence.com Rankings

Tai-Ping Liu

Physics

#4371

World Rank

#6020

Historical Rank

#1469

USA Rank

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Physics

Tai-Ping Liu's Degrees

PhD Physics California Institute of Technology
Masters Physics California Institute of Technology

Why Is Tai-Ping Liu Influential?

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According to Wikipedia, Tai-Ping Liu is a Taiwanese mathematician, specializing in partial differential equations. Liu received his bachelor's degree in mathematics in 1968 from National Taiwan University, his master's degree in 1970 from Oregon State University, and his PhD in 1973 from University of Michigan with thesis advisor Joel Smoller and thesis Riemann problem for general 2 × 2 systems of conservation laws. Afterwards Liu was a professor at University of Maryland, from 1988 at New York University and from 1990 at Stanford University, where he is now retired. Since 2000 he has been a Distinguished Research Fellow at the Academia Sinica. He was elected a Fellow of the American Mathematical Society in 2012.

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Tai-Ping Liu's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Hyperbolic conservation laws with stiff relaxation terms and entropy (1994) (724)
Hyperbolic conservation laws with relaxation (1987) (578)
Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping (1992) (356)
Nonlinear Stability of Shock Waves for Viscous Conservation Laws (1985) (344)
The Riemann problem for general systems of conservation laws (1975) (282)
Boltzmann Equation: Micro-Macro Decompositions and Positivity of Shock Profiles (2004) (261)
Vacuum states for compressible flow (1997) (259)
Admissible solutions of hyperbolic conservation laws (1981) (236)
The Riemann problem for general 2×2 conservation laws (1974) (232)
Quasilinear hyperbolic systems (1979) (222)
Energy method for Boltzmann equation (2004) (221)
L1 Stability Estimates for n×n Conservation Laws (1999) (219)
The Pointwise Estimates of Diffusion Wave for the Navier–Stokes Systems in Odd Multi-Dimensions (1998) (214)
The deterministic version of the Glimm scheme (1977) (193)
Large Time Behavior of Solutions for General Quasilinear Hyperbolic-Parabolic Systems of Conservation Laws (1997) (192)
Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations (1979) (191)
Pointwise convergence to shock waves for viscous conservation laws (1997) (165)
The entropy condition and the admissibility of shocks (1976) (153)
Nonlinear stability of rarefaction waves for compressible Navier Stokes equations (1988) (150)
Compressible flow with damping and vacuum (1996) (138)
Zero relaxation and dissipation limits for hyperbolic conservation laws (1993) (133)
Source-Solutions and Asymptotic Behavior in Conservation Laws. (1984) (129)
The Green's function and large‐time behavior of solutions for the one‐dimensional Boltzmann equation (2004) (129)
Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves (1998) (123)
Particle-like solutions of the Einstein-Yang Mills equations and the existence of an exotic black-hole solution (1996) (121)
Solutions of Euler-Poisson Equations¶for Gaseous Stars (2002) (120)
Nonlinear stability and instability of transonic flows through a nozzle (1982) (119)
Existence theory for nonlinear hyperbolic systems in nonconservative form (1993) (118)
Well‐posedness theory for hyperbolic conservation laws (1999) (115)
On the vacuum state for the isentropic gas dynamics equations (1980) (113)
Supersonic flow onto a solid wedge (2007) (110)
Nonlinear resonance for quasilinear hyperbolic equation (1987) (108)
Linear and nonlinear large-time behavior of solutions of general systems of hyperbolic conservation laws (1977) (108)
Compressible Euler Equations with Vacuum (1997) (107)
Advances in the Theory of Shock Waves (2001) (105)
The inviscid limit for the Navier-Stokes equations of compressible, isentropic flow with shock data (1989) (104)
Decay to N-waves of solutions of general systems of nonlinear hyperbolic conservation laws (1977) (103)
Shock waves for compressible navier‐stokes equations are stable (1986) (95)
Nonlinear Stability of Rarefaction Waves for the Boltzmann Equation (2006) (83)
Transonic gas flow in a duct of varying area (1982) (78)
ASYMPTOTIC BEHAVIOR FOR SCALAR VISCOUS CONSERVATION LAWS WITH BOUNDARY EFFECT (1997) (78)
The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow (1984) (78)
Pointwise decay to contact discontinuities for systems of viscous conservation laws (1997) (73)
Initial-boundary value problems for gas dynamics (1977) (67)
Nonlinear Stability of a Self-Similar 3-Dimensional¶Gas Flow (1999) (67)
Propagation of a Stationary Shock Layer in the Presence of a Boundary (1997) (64)
Recent Mathematical Methods in Nonlinear Wave Propagation (1996) (64)
Riemann Problems for Reacting Gas, with Applications to Transition (1982) (63)
On nonlinear stability of general undercompressive viscous shock waves (1995) (62)
Nonlinear stability of an undercompressive shock for complex Burgers equation (1995) (61)
Large-time behavior of solutions of initial and initial-boundary value problems of a general system of hyperbolic conservation laws (1977) (61)
Comprenssible flow with vacumm and phisycal singlarity (2000) (59)
Convergence to diffusion waves of solutions for viscous conservation laws (1987) (58)
Invariants and asymptotic behavior of solutions of a conservation law (1978) (57)
On a nonstrictly hyperbolic system of conservation laws (1985) (55)
Initial‐boundary value problem for one‐dimensional wave solutions of the Boltzmann equation (2007) (55)
Shock Waves in Conservation Laws With Physical Viscosity (2015) (51)
Uniqueness of weak solutions of the Cauchy problem for general 2 × 2 conservation laws (1976) (50)
Time-Asymptotic Behavior of Wave Propagation Around a Viscous Shock Profile (2009) (50)
Green's Function of Boltzmann Equation, 3-D Waves (2006) (50)
Hyperbolic and viscous conservation laws (2000) (48)
Nonlinear stability of overcompresive shock waves in a rotationally invariant system of viscous conservation laws (1993) (48)
Thermal transpiration for the linearized Boltzmann equation (2007) (46)
₁ stability for 2×2 systems of hyperbolic conservation laws (1999) (46)
Compressible Navier–Stokes Equations with Zero Heat Conductivity (1999) (43)
A NEW ENTROPY FUNCTIONAL FOR A SCALAR CONSERVATION LAW (1999) (43)
Nonlinear stability of strong detonations for a viscous combustion model (1995) (42)
Invariant Manifolds for Steady Boltzmann Flows and Applications (2013) (39)
Travelling waves in hyperelastic rods (1979) (39)
Continuum shock profiles for discrete conservation laws I: Construction (1999) (38)
SOLVING BOLTZMANN EQUATION, PART I: GREEN'S FUNCTION (2011) (36)
L_1 Stability of Conservation Laws with coinciding hugoniot and characteristic curves (1999) (35)
Existence and uniqueness theorems for Riemann problems (1975) (34)
Stability of shock waves for the Broadwell equations (1988) (33)
Weak Solutions of General Systems of Hyperbolic Conservation Laws (2002) (33)
Existence of boundary layer solutions to the Boltzmann equation (2004) (31)
Nonlinear Stability of Weak Detonation Waves¶for a Combustion Model (1999) (30)
A scalar combustion model (1991) (29)
THE ELLIPTICITY PRINCIPLE FOR SELF-SIMILAR POTENTIAL FLOWS (2005) (28)
Large-Time Behavior of Solutions for the Boltzmann Equation with Hard potentials (2006) (28)
Resonance for quasilinear hyperbolic equation (1982) (26)
Entropy Production and Admissibility of Shocks (2003) (25)
Wave propagation for the compressible Navier–Stokes equations (2015) (24)
Boundary Singularity for Thermal Transpiration Problem of the Linearized Boltzmann Equation (2014) (24)
Shock waves in the nonisentropic gas flow (1976) (23)
ON BOUNDARY RELATION FOR SOME DISSIPATIVE SYSTEMS (2011) (23)
Stability of viscous shock waves associated with a system of nonstrictly hyperbolic conservations laws (1992) (21)
Free Molecular Flow with Boundary Effect (2013) (20)
On a Hyperbolic System of Conservation Laws Which Is Not Strictly Hyperbolic. (1981) (19)
L1 STABILITY FOR 2× 2 SYSTEMS OF HYPERBOLIC CONSERVATION LAWS (1999) (18)
NONLINEAR STABILITY AND INSTABILITY OF OVERCOMPRESSIVE SHOCK WAVES (1993) (18)
Overcompressive shock waves (1990) (18)
CONTINUUM SHOCK PROFILES FOR DISCRETE CONSERVATION LAWS II: STABILITY (1999) (17)
Stability of Strong Detonation Travelling Waves to Combustion Model (1996) (16)
The free piston problem for gas dynamics (1978) (16)
Nonlinear singular sturm-liouville problems and an application to transonic flow through a nozzle (1990) (16)
Asymptotic states for hyperbolic conservation laws with a moving source (1983) (15)
Viscosity criterion for hyperbolic conservation laws (1991) (15)
Improvement on Stability Analysis for Linear Systems Under State Saturation (2008) (15)
DIRICHLET-NEUMANN KERNEL FOR HYPERBOLIC-DISSIPATIVE SYSTEM IN HALF-SPACE (2012) (14)
Equilibrating Effects of Boundary and Collision in Rarefied Gases (2014) (14)
Nonlinear hyperbolic-dissipative partial differential equations (1996) (13)
L 1 STABILITY FOR 2 × 2 SYSTEMS OF HYPERBOLIC CONSERVATION LAWS (1999) (13)
Physicality of Weak Prandtl-Meyer Reflection(Mathematical Analysis in Fluid and Gas Dynamics : A conference in honor of Professor Tai-Ping Liu on his 60th Birthday) (2006) (12)
VISCOUS RAREFACTION WAVES (2010) (12)
A conservative, piecewise-steady difference scheme for transonic nozzle flow (1986) (11)
Singularity of the Velocity Distribution Function in Molecular Velocity Space (2016) (10)
The ellipticity principle for steady and selfsimilar polytropic potential flow (2004) (10)
Nonlinear waves for viscoelasticity with fading memory (1988) (10)
Convergence and error bound analysis of a finite-difference scheme for the one-dimensional Navier-Stokes equations (1996) (9)
Contributions to the mathematical theory of magnetohydrodynamic shock waves (1996) (9)
Diffusion under gravitational and boundary effects. (2008) (9)
Propagation of Viscous Shock Waves Away from the Boundary (2004) (9)
ON GREEN＇S FUNCTION FOR HYPERBOLIC-PARABOLIC SYSTEMS (2009) (9)
MULTI-DIMENSIONAL GAS FLOW: SOME HISTORICAL PERSPECTIVES (2011) (7)
Nonlinear Evolutionary Partial Differential Equations (1996) (7)
Uniform $L_1$ boundedness of solutions of hyperbolic conservation laws (1997) (7)
Nonlinear Waves in Mechanics and Gas Dynamics. (1997) (7)
Stability of boundary integral methods for water waves (1996) (6)
Zero dissipation and stability of shocks (1998) (6)
The essence of Glimm’s scheme (1996) (6)
Navier‐Stokes Equations in Gas Dynamics: Green's Function, Singularity, and Well‐Posedness (2021) (6)
VISCOUS SHOCK WAVE TRACING, LOCAL CONSERVATION LAWS, AND POINTWISE ESTIMATES (2009) (6)
Mixture Lemma (2010) (6)
On the spherically symmetric motion of self-gravitating isentropic gas surrounding a solid ball (1996) (5)
Boundary Wave Propagator for Compressible Navier–Stokes Equations (2014) (5)
Letter to the editors in chief (2017) (5)
Singular perturbation problems to a combustion equation in very long cylindrical domains (1996) (5)
Multi-dimensional Wave Propagation Over a Burgers Shock Profile (2018) (5)
Boltzmann collision operator for the infinite range potential: A limit problem (2019) (4)
On the stability of Broadwell shocks (1996) (4)
VISCOUS CONSERVATION LAWS, PART I: SCALAR LAWS (2010) (4)
Boltzmann equation, boundary effects (2009) (4)
Well-Posedness Theory for Hyperbolic Systems of Conservation Laws (2001) (3)
Hyperbolic conservation laws and dynamic systems (1999) (3)
A symplectic difference scheme for the PDEs (1996) (3)
Discontinuous solutions of the Navier-Stokes equations for multidimensional, compressible flow (1996) (3)
ON SHOCK WAVE THEORY (2000) (3)
Uniform L1 boundedness of solutions of hyperbolic conservation laws (1997) (3)
Nonlinear waves for viscous conservation laws (1996) (2)
Asymptotic configuration of stationary interfacial patterns for reaction diffusion systems (1996) (2)
Survey of vacuum theory and conjecture (1996) (2)
SELF-SIMILAR SOLUTIONS OF 2-D COMPRESSIBLE EULER EQUATIONS AND MIXED-TYPE PROBLEMS (2015) (2)
Entropy for hyperbolic systems of conservation laws in several space dimensions (1996) (2)
On the compactly supported solutions of KPP or Fischer type equations (1996) (2)
The ellipticity principle for selfsimilar polytropic potential flow (2005) (2)
Scattering operator for the Klein-Gordon equation on the Schwarzschild metric (1996) (2)
Multiscale structure for hyperbolic waves (1996) (2)
Solution to M-D Riemann problems for quasilinear hyperbolic system of proportional conservation laws (1996) (2)
Resonances of the Schwarzschild metric (1996) (1)
FUJITA EQUATION WITH BOUNDARY EFFECT (2014) (1)
The large time behavior of Cauchy problem for a dissipative Benjamin-Ono type equation (1996) (1)
A new framework of nonlinear hydrodynamics (1996) (1)
Convergence of diffusion waves of solutions for viscous conservation laws (1989) (1)
Global existence and qualitative behavior of solutions for the system of compressible adiabatic flow with damping (1996) (1)
Optimal error estimates for viscosity method and monotone scheme to Riemann problem (1996) (1)
Invariant Manifolds for Steady Boltzmann Flows and Applications (2013) (1)
Slow dynamics of linear waves in nonlinear systems of conservation laws (1996) (1)
Euler-Poisson-Darboux equations and hyperbolic conservation laws (1996) (1)
Nonlinear Galerkin method for Navier-Stokes equations with stream form (1996) (1)
The Green Function and Large-Time Behavior of Solutions of the Boltzmann Equation and Planar Waves (2004) (1)
Aspects of dissipation for compressible fluids and kinetic theory (2013) (1)
Shock waves in Euler equations for compressible medium (2021) (1)
Nonlinear Galerkin method using Legendre polynomials (1996) (1)
Stability for Systems of Hyperbolic Conservation Laws (1999) (1)
Stability of Nonlinear Waves (1987) (1)
Geometric Theory of Shock Waves (1991) (1)
Nonlinear evolutionary partial differential equations : International Conference on Nonlinear Evolutionary Partial Differential Equations, June 21-25, 1993, Beijing, People's Republic of China (1997) (1)
Smooth shock profiles in viscoelasticity with memory (1996) (1)
Well-Posedness Theory for System of Hyperbolic Conservation Laws (1999) (1)
A new proof of existence of the wave front solutions for a kind of reaction-diffusion system (1996) (1)
Some problems on semiconductor equations (1996) (1)
On Nonlinear Stability of Viscous Shock Waves with Physical Viscosity (2012) (1)
Weak linear degeneracy and global existence of classical solutions for quasilinear hyperbolic systems (1996) (0)
The zero dispersion limit, a deterministic analogue of turbulence (1996) (0)
A degenerate reaction-diffusion problem (1996) (0)
A stationary solution for a ﬂuid dynamical model of semiconductor (2018) (0)
in for the (2018) (0)
Nonexistence of global solutions to a class of generalized improved Boussinesq equations (1996) (0)
Geometric theory of shock waves. Multidimensional hyperbolic problems and computations (1989) (0)
Delta waves in solutions of conservation laws (1996) (0)
A study of the global weak solution for the isentropic equation of a polytropic gas (1996) (0)
Study on Fault-Tolerant Technique Based on Knowledge Modules of Hydraulic Fault Theory (2013) (0)
Cauchy problem for strongly damped nonlinear wave equations (1996) (0)
Boundary Singularity for Thermal Transpiration Problem of the Linearized Boltzmann Equation (2014) (0)
Multidimensional shock-waves for relativistic fluids (1996) (0)
Interaction of three progressing waves with different singularities for semilinear wave equations (1996) (0)
Green’s function of heat equation for heterogeneous media in 3-D (2022) (0)
Global existence of solutions for the reaction-diffusion systems which don’t satisfy a zero sum condition (1996) (0)
Energy Method for Equations in Gas Dynamics (2003) (0)
A survey on stability of viscous shock profiles without genuine nonlinearity (1996) (0)
Analytic solutions of Belousov-Zhabotinskii reaction (1996) (0)
Singularity of the Velocity Distribution Function in Molecular Velocity Space (2015) (0)
Resonance for Quasilinear Hyperbolic Equation by Tai-ping Liu (2007) (0)
Existence and nonexistence of global solution of nonlinear parabolic equation with nonlinear boundary condition (1996) (0)
Boundary Wave Propagator for Compressible Navier–Stokes Equations (2013) (0)
Systems of quasilinear hyperbolic equations with quadratic coupling (1996) (0)
On a complex dynamical and dissipative structure of partial differential equations (1996) (0)
On Recent Progress in Shock Wave Theory (2000) (0)
Vacuum problem for the damped p-system (1996) (0)
Free Molecular Flow with Boundary Effect (2013) (0)
HYPERBOLIC CONSERVATION LAWS AND RELATED TOPICS (1987) (0)
Multi-dimensional Wave Propagation Over a Burgers Shock Profile (2018) (0)
Some results on nonlinear evolution equations (1996) (0)
Entropy solutions for a hydrodynamic model for semiconductors (1996) (0)
The global attractors for the Landau-Lifshitz equation of the ferromagnetic spin chain on compact manifolds (1996) (0)
STABILITY OF VISCOUS SHOCK WAVES (Mathematical Analysis in Fluid and Gas Dynamics) (2010) (0)
Zeros of solutions of hyperbolic equations with functional arguments (1996) (0)
Existence and convergence of solutions to higher order generalized KdV-Burgers equations (1996) (0)
BV SOLUTIONS FOR HYPERBOLIC BALANCE LAWS WITH PERIODIC INITIAL DATA (2016) (0)
Proceedings of the XV international conference on hyperbolic problems: Theory, numerics, applications (2016) (0)
Periodic boundary value problem and Cauchy problem for generalized IMBq equation with several variables (1996) (0)
Stability of Transonic Flows along a Nozzle. (1981) (0)
Nonlinear Partial Differential Equations for Gas and Elasticity (1990) (0)
Spirals for Riemann problems in multipieces for 2-D Euler equations by using MmB schemes (1996) (0)
1. Hyperbolic Conservation Laws (2000) (0)
Necessary and sufficient conditions of extinction and blow-up on some parabolic equations (1996) (0)
Riemann problem for hyperbolic combustion (1996) (0)
D EXISTENCE AND UNIQUENESS THEOREMS FOR RIEMANN PROBLEMS (2010) (0)
Physicality of Weak Prandtl-Meyer Reflection(Mathematical : (2018) (0)
Shock and boundary layer behavior of solutions to the Broadwell equation in the fluid dynamic limit (1996) (0)
Title Cylindrical Couette flow of a vapor-gas mixture:A ghost effect in the continuum limit(Mathematical Analysis in Fluid and Gas Dynamics : A conference in honor of Professor Tai-Ping Liu on his 60th Birthday) (2016) (0)
Some Nonlinear Functionals for Scalar Conservation Laws (2001) (0)
Shock Waves (2003) (0)
2. Viscous Conservation Laws (2000) (0)
Non-Linear Waves in Gas Dynamics and Mechanics (1994) (0)
Existence and uniqueness of global solution for certain degenerate reaction-diffusion systems (1996) (0)
A combined spectral-finite element method for a type of nonlinear two-dimensional Schrödinger equations (1996) (0)
Nonlinear system of equations of mixed type and nonlinear complex equation of mixed type (1996) (0)
Kinetic Theory and Gas Dynamics, Some Historical Perspectives (2014) (0)
Finite dimensionality of attractors of magnetic flow equation (1996) (0)
Large time step Glimm’s and Godunov’s schemes and their entropy consistency (1996) (0)
Partial dissipation and sub-shock (2023) (0)
Global behavior of positive solutions to a quasilinear parabolic equation with nonlinear boundary absorption (1996) (0)
Equilibrating Effects of Boundary and Collision in Rarefied Gases (2014) (0)
1989 Conference on Nonlinear Analysis, Academia Sinica, Taipei, Republic of China, 19-24 June, 1989 (1991) (0)
Cauchy problem of nonisentropic gas dynamics equations (1996) (0)
Viscous Scalar Rarefaction Waves (2017) (0)
Dynamics on the attractor for reaction-diffusion systems in higher space dimensions (1996) (0)
The bidimensional Stefan problem with nonlinear convection (1996) (0)

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