Some of Publications by Gui-Qiang Chen

Books:

1998: Advances in Nonlinear Partial Differential Equations and Related Areas, World Scientific Publishing Co Pte Ltd, ISBN: 981-02-3664-6 (Edited with Y.-Y. Li, X.-P. Zhu, and D.-M. Cao).
1999: Nonlinear Partial Differential Equations. Contemporary Mathematics, 238, AMS: Providence, ISBN 0-8218-1196-7 (Edited with E. DiBenedetto).
2005: Nonlinear Partial Differential Equations and Related Analysis. Contemporary Mathematics, 371, AMS: Providence, ISBN 0-8218-3533-5 (Edited with G. Gasper and J. Jerome).
2007: Stochastic Analysis and Partial Differential Equations, Contemporary Mathematics, AMS: Providence, about 300 pages (in press) (Edited with E. Hsu and M. Pinsky).

Lecture Notes:

2000: Compactness Methods and Nonlinear Hyperbolic Conservation Laws
2001: On the Theory of Divergence-Measure Fields and Its Applications (with Herman Frid)
2002: The Cauchy Problem for the Euler Equations for Compressible Fluids (with Dehua Wang)
2003: Some Recent Methods for Partial Differential Equations of Divergence Form
2005: Euler Equations and Related Hyperbolic Conservation Laws
2006: Compressible Flows: Mathematical Theory
2007: Measure-Theoretical Analysis and Nonlinear Conservation Laws(with Monica Torres and William Ziemer)

Survey and Conference Papers:

Some of Original Research Papers:

1992: The Method of Quasidecoupling for Discontinuous Solutions to Conservation Laws
1993: Spectral Viscosity Approximations to Multidimensional Scalar Conservation Laws (with Qiang Du and Eitan Tadmor)
1994: Hyperbolic Conservation Laws with Stiff Relaxation Terms and Entropy (with David Levermore and Tai-Ping Liu)
1995: Hyperbolic Conservation Laws with Umbilic Degeneracy (I) (with Pui Tak Kan)
1997: Convergence of Difference Schemes with High Resolution for Conservation Laws (with Jian-Guo Liu)
1999a: Decay of Entropy Solutions of Nonlinear Conservation Laws (with Hermano Frid)
1999b: Large-Time Behavior of Entropy Solutions of Conservation Laws (with Hermano Frid)
1999c: Divergence-Measure Fields and Hyperbolic Conservation Laws (with Hermano Frid)
1999d: Vanishing Viscosity Limit for Initial-Boundary Value Problem for Conservation Laws (with Hermano Frid)
2000a: Compressible Euler Equations with General Pressure Law (with Philippe LeFloch)
2000b: Discontinuous Solutions in $L^{\infty}$ for Hamilton-Jacobi Equations (with Bo Su)
2000c: Initial Layers and Uniqueness of Solutions to Conservation Laws (with Michel Rascle)
2000d: Global Solutions of the Compressible Navier-Stokes Equations with Large Discontinuous Initial Data (with David Hoff and Konstantina Trivisa)
2000e: Vacuum States and Global Stability of Rarefaction Waves for Compressible Flow
2001a: Uniqueness and Asymptotic Stability of Riemann Solutions for the Compressible Euler Equations (with Hermano Frid)
2001b: Stability of Entropy Solutions to the Cauchy Problem for a Class of Hyperbolic-Parabolic Equations (with Emmanuele DiBenedetto)
2001c: On the Zero-Rossby Limit for the Primitive Equations of Atmosphere (with Ping Zhang)
2001d: Hyperbolic Conservation Laws with Umbilic Degeneracy (II) (with Pui Tak Kan)
2002a: Uniqueness and Stability of Riemann Solutions with Large Oscillation in Gas Dynamics (with Hermano Frid and Yachun Li)
2002b: Global Solutions to the Navier-Stokes Equations for Compressible Heat-Conducting Flow with Symmetry and Free Boundary (with Milan Kratka)
2002c: Global Solutions of Nonlinear Magnetohydrodynamics with Large Initial Data (with Dehua Wang)
2002d: On the Navier-Stokes Equations for Exothermically Reacting Compressible Fluids (with David Hoff and Konstantina Trivisa)
2003a: Well-Posedness for Anisotropic Degenerate Parabolic-Hyperbolic Equations (with Benoit Perthame)
2003b: Formation of Delta-Shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Isentropic Euler Equations (with Hailiang Liu)
2003c: Existence Theory for the Isentropic Euler Equations (with Philippe LeFloch)
2003d: Multidimensional Transonic Shocks and Free Boundary Problems for Nonlinear Equations of Mixed-Type (with Mikhail Feldman)
2003e: Global Solutions to A Model For Exothermically Reacting, Compressible Flows with Large Discontinuous Initial Data (with David Hoff and Konstantina Trivisa)
2003f: Extended Divergence-Measure Fields and the Euler Equations for Gas Dynamics (with Hermano Frid)
2003g: Global Entropy Solutions to Exothermically Reacting, Compressible Euler Equations (with David Wagner)
2003h: A Viscous Approximation for a Multidimensional Unsteady Euler Flow: Existence Theorem for Potential Flow (with Bo Su)
2003i: Global Entropy Solutions in $L^\infty$ to the Euler Equations and Euler-Poisson Equations for Isothermal Fluids with Spherical Symmetry(with Tianhong Li)
2004a: Steady Transonic Shocks and Free Boundary Problems in Infinite Cylinders for the Euler Equations (with Mikhail Feldman)
2004b: Concentration and Cavitation in the Vanishing Pressure Limit of Solutions to the Euler Equations for Nonisentropic Fluids (with Hailiang Liu)
2004c: Entropy Solutions in $L^\infty$ for the Euler Equations in Nonlinear Elastodynamics and Related Equations(with Banghe Li and Tianhong Li)
2004d: L-1 Framework for Continuous Dependence and Error Estimates for Quasilinear Anisotropic Degenerate Parabolic Equations (with Knneth Karlsen)
2004e: Free Boundary Problems and Transonic Shocks in Unbounded Domains (with Mikhail Feldman)
2004f: Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws(with Monica Torres)
2004g: Stability of Riemann Solutions with Large Oscillation for the Relativistic Euler Equations(with Yachun Li)
2005a: Potential Theory for Shock Reflection by a Large-Angle Wedge(with Mikhail Feldman)
2005b: Validity of Nonlinear Geometric Optics for Entropy Solutions of Multidimensional Scalar Conservation Laws (with Stephane Junca and Michel Rascle)
2005c: Existence and Stability of Supersonic Euler Flows past Lipschitz Wedges(with Yongqian Zhang and Dianwen Zhu)
2005d: Existence and Stablity of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections(with Mikhail Feldman)
2005e: Global Solutions to Shock Reflection by Large-Angle Wedges for Potential Flow(with Mikhail Feldman)
2006a: On Two-Dimensional Sonic-Subsonic Flow(with Constantine Dafermos, Marshall Slemrod, and Dehua Wang)
2006b: Existence and Stability of Supersonic Vortex Sheets in Euler Flows past Lipschitz Walls (with Yongqian Zhang and Dianwen Zhu)
2006c: Hydrodynamic Limit for Particle Systems and Related Conservation Laws with Discontinuous Fluxes(with Nadine Even and Christian Klingenberg)
2006c: Dependence of Entropy Solutions in the Large for the Euler Equations on Nonlinear Flux Functions(with Cleopatra Christoforou and Yongqian Zhang)
2006d: Well-Posedness for Two-Dimensional Steady Supersonic Euler(with Tianhong Li)
2006e: Existence and Stability of Compressible Current-Vortex Sheets in Three-Dimensional Magnetohydrodynamics(with Yaguang Wang)
2006f: Vanishing Viscosity Method for Transonic Flow(with Marshall Slemrod and Dehua Wang)
2007a: Hyperbolic Conservation Laws with Discontinuous Fluxes and Hydrodynamic Limit for Particle Systems(with Nadine Even and Christian Klingenberg)
2007b: Gauss-Green Theorem for Weakly Differential Fields, Sets of Finite Perimeter, and Balance Laws(with Monica Torres and William Ziemer)