Scientific Papers by Gui-Qiang G. Chen

 

Some Original Papers:

 

       

 

 

1.      G.-Q. Chen & M. Feldman:  Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures, Research Monograph, pp. 750±, Preprint, 2015.

 

2.      G.-Q. Chen & M. Perepelitsa:  Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data, Communications in Mathematical Physics, 338 (2015), 771800.

 

3.      G.-Q. Chen, F. Huang & T.-Y. Wang:  Subsoni-Sonic Limit of Approximate Solutions to Multidimensional Steady Euler Equations, Archive for Rational Mechanics and Analysis, 2015 (to appear); Preprint, arXiv:1311.3985 (2014).       

 

4.      G.-Q. Chen, C. Xiao & Y. Zhang:  Existence of entropy solutions to two-dimensional steady exothermically reacting Euler equations, Acta Mathematica Scientia, 34B (2014), 1–38.

 

5.      G.-Q. Chen, X. Deng & W. Xiang:  Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System, Archive for Rational Mechanics and Analysis, 211 (2014), 61—112.

 

6.      G.-Q. Chen, W. Xiang & Y. Zhang:  Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws, Communications in Partial Differential Equations, 38 (2013), 1936—1970.

 

7.      G.-Q. Chen, V. Kukreja & H. Yuan:  Stability of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows, Journal of Mathematical Physics, 54 (2013), 2515—2542.

 

8.      G.-Q. Chen, V. Kukreja & H. Yuan:  Well-Posedness of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows, Zeitschrift für angewandte Mathematik und Physik, 64 (2013), 1711—1727.

 

9.      M. Bae, G.-Q. Chen & M. Feldman:  Prandtl-Meyer Reflection for Supersonic Flow past a Solid Ramp, Quart. Appl. Math. 71 (2013), 583—600 (In honor of Costas Dafermos on the occasion of his 70th birthday).

 

10.  G.-Q. Chen & H. Yuan:  Local Uniqueness of Steady Spherical Transonic Shock-fronts for the Three-Dimensional Full Euler Equations, Communications on Pure and Applied Analysis, 12 (2013), 2515—2542.

 

11.  G.-Q. Chen, X. Deng & W. Xiang:  Global Steady Subsonic Flows through Infinitely Long Nozzles for the Full Euler Equations, SIAM Journal on Mathematical Analysis, 44 (2013), 2888—2919.

 

12.  G.-Q. Chen & M. Feldman:  Comparison Principles for Self-Similar Potential Flow, Proceedings of the American Mathematical Society, 140 (2012), 651—663.

 

13.  G.-Q. Chen & J. Glimm:  Kolmogorov's Theory of Turbulence and Inviscid Limit of the Navier-Stokes Equations in R3, Communications in Mathematical Physics,  310 (2012), 267—283.

 

14.  G.-Q. Chen & M. Perepelitsa:  Shallow Water Equations: Viscous Solutions and Inviscid Limit, Zeitschrift für angewandte Mathematik und Physik (ZAMP),  63 (2012), 1067—1084.

 

15.  G.-Q. Chen & Y. Wang: Characteristic Discontinuities and Free Boundary Problems for Hyperbolic Conservation Laws, In: Nonlinear Partial Differential Equations, The Abel Symposium 2010, Chapter 5, pp. 53—82, H. Holden & K.H. Karlsen (Eds.), Springer, 2012.

 

16.  G.-Q. Chen, Q. Ding & K.K. Karlsen:  On Nonlinear Stochastic Balance Laws, Archive for Rational Mechanics and Analysis, 204 (2012), 707—743.

 

17.  G.-Q. Chen & M. Torres:  On the Structure of Solutions of Nonlinear Hyperbolic Systems of Conservation Laws, Communications on Pure and Applied Analysis, 10 (2011), 1011—1036.

 

18.  G.-Q. Chen & M. Perepelitsa: Vanishing Viscosity Limit of the Navier-Stokes Equations to the Euler Equations, Comm. Pure Appl. Math.  63 (2010), 1469—1504.

 

19.  G.-Q. Chen & M. Feldman: Global Solutions to Shock Reflection by Large-Angle Wedges for Potential Flow, Annals of Mathematics, 171 (2010), 1067—1182.

 

20.  G.-Q. Chen & M. Perepelitsa: Vanishing Viscosity Limit of the Navier-Stokes Equations to the Euler Equations, Communications on Pure and Applied Mathematics, 63 (2010), 1469—1504.

 

21.  G.-Q. Chen, M. Slemrod & D. Wang: Weak Continuity of the Gauss-Codazzi-Ricci Equations for Isometric Embedding, Proceedings of the American Mathematical Society, 138 (2010), 1843—1851.

 

22.  G.-Q. Chen & W. Ruan:  A Hyperbolic System of Conservation Laws for Fluid Flows through Compliant Axisymmetric Vessels, Acta Mathematica Scientia, 30B(2) (2010), 391—427 (Invited paper).

 

23.  G.-Q. Chen & Z.-M. Qian:  A Study of the Navier-Stokes Equations with Kinematic and Navier Boundary Conditions, Indiana University Mathematics Journal, 59 (2010), 721—760.

 

24.  G.-Q. Chen, M. Slemrod & D. Wang: Isometric Immersion and Compensated Compactness, Communications in Mathematical Physics, 294 (2010), 411—437.

 

25.  M.-J. Bae, G.-Q. Chen & M. Feldman:  Regularity of Solutions to Regular Shock Reflection for Potential Flow, Inventiones Mathematicae, 175 (2009), 505—543.

 

26.  G.-Q. Chen & B.-X. Fang:  Stability of Transonic Shock-Fronts in Steady Potential Flow past a Perturbed Cone, Discrete and Continuous Dynamical Systems, 23 (2009), 85—114.

 

27.  G.-Q. Chen & H.-R. Yuan:  Uniqueness of Transonic Shock Solutions in a Duct for Steady  Potential Flow, Journal of Differential Equations, 247 (2009),  564—573.

 

28.  G.-Q. Chen, D. Osborne & Z.-M. Qian:  The Navier-Stokes Equations with the Kinematic and Vorticity Boundary Conditions on Non-Flat Boundaries, Acta Mathematica Scientia, 29B(4) (2009), 919—948  (Invited paper).

 

29.  G.-Q. Chen, M. Torres & W. Ziemer:  Gauss-Green Theorem for Weakly Differentiable Fields, Sets of  Finite Perimeter, and Balance Laws,       Communications on Pure and Applied Mathematics, 62 (2009), 242—304.

 

30.  G.-Q. Chen, D. Wang & X.-Z. Yang:  Evolution of Discontinuity and Triple Shock Structure for a Two-dimensional Hyperbolic System of Conservation Laws, SIAM Journal on Mathematical Analysis, 41 (2009), 1—25.

 

31.  G.-Q. Chen & B. Perthame:  Large Time Behavior of Periodic Solutions to Anisotropic Degenerate Parabolic-Hyperbolic Equations, Proceedings of the American Mathematical Society, 137 (2009), 3003—3011.

 

32.  G.-Q. Chen, C. Christoforou & Y.-Q.  Zhang:  Continuous Dependence of Entropy Solutions to the Euler Equations with respect to the Adiabatic Exponent and Mach Number, Archive for Rational Mechanics and Analysis,  189 (2008), 97—130.

 

33.  G.-Q. Chen & T.-H. Li:  Well-Posedness for Two-Dimensional Steady Supersonic Euler Flows past a Lipschitz Wedge, Journal of Differential Equations, 244 (2008), 1521—1550.

 

34.  G.-Q. Chen, M. Slemrod & D. Wang: Vanishing Viscosity Method for Transonic Flow, Archive for Rational Mechanics and Analysis, 189 (2008), 159—188.

 

35.  G.-Q. Chen, N. Even & C. Klingenberg:  Hyperbolic Conservation Laws with Discontinuous Fluxes and Hydrodynamic Limit for Particle Systems, Journal of Differential Equations, 245 (2008), 3095—3126.

 

36.  G.-Q. Chen, Y. Zhang & D. Zhu:  Existence and Stability of Supersonic Vortex Sheets in Euler Flows past Lipschitz Walls,  SIAM Journal on Mathematical Analysis, 38 (2007), 1660—1693.

 

37.  G.-Q. Chen, C.M. Dafermos, M. Slemrod & D. Wang:  On Two-Dimensional Sonic-Subsonic Flow, Communications in Mathematical Physics, 271 (2007), 635—647.

 

38.  G.-Q. Chen, M. Torres & W. Ziemer: Measure-Theoretical Analysis and Nonlinear Conservation Laws, Pure and Applied Mathematics Quarterly, 3 (2007), 841—879 (Invited paper).

 

39.  G.-Q. Chen & M. Feldman: Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections, Archive for Rational Mechanics and Analysis, 184 (2007), 185—242. 

 

40.  G.-Q. Chen & J. Chen:  Stability of Plane Rarefaction Waves and Vacuum States for the Multidimensional Euler Equations for Compressible Fluids, Journal of Hyperbolic Differential Equations, 4 (2007), 105—122.

 

41.  G.-Q. Chen, J. Chen & M. Feldman:  Transonic Shocks and Free Boundary Problems for the Full Euler Equations in Infinite Nozzles, Journal de Mathématiques Pures et Appliquées, 88 (2007), 191—218.

 

42.  G.-Q. Chen & C. Christoforou:  Solutions for a Nonlocal Conservation Law with Fading Memory, Proceedings of the American Mathematical Society, 135 (2007), 3905—3915.

 

43.  G.-Q. Chen, C. Christoforou & Y.-Q. Zhang:  Dependence of Entropy Solutions in the Large for the Euler Equations on Nonlinear Flux Functions, Indiana University Mathematics Journal, 56 (2007), 2535—2568.

 

44.  G.-Q. Chen & Y.-G. Wang:  Existence and Stability of Compressible Current-Vortex Sheets in Three-Dimensional Magnetohydrodynamics, Archive for Rational Mechanics and Analysis, 187 (2007), 369—408.

 

45.  A. Chen, G.-Q. Chen & R.A. Freeman:  Stability of Nonlinear Feedback Systems: New Small-Gain Theorem, SIAM Journal on Control and Optimization (SICON), 46 (2007),  1995—2012.

 

46.  G.-Q. Chen & K.H. Karlson: Continuous Dependence and Error Estimates for Quasilinear Degenerate Parabolic Equations: Kinetic Approach, Transactions of the American Mathematical Society, 358 (2006), 937—963.

 

47.  G.-Q. Chen, S. Junca & M. Rascle: Validity of Nonlinear Geometric Optics for Entropy Solutions of Multidimensional Conservation Laws,       Journal of Differential Equations, 222 (2006), 439—475.

 

48.  G.-Q. Chen, Y. Zhang & D. Zhu: Existence and Stability of Supersonic Euler Flows past Lipschitz Wedges, Archive for Rational Mechanics and Analysis, 181 (2006), 261—310.

 

49.  G.-Q. Chen & M. Torres, Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws, Archive for Rational Mechanics and Analysis, 175 (2005), 245—267.

 

50.  G.-Q. Chen & K.H. Karlsen: Quasilinear Anisotropic Degenerate Parabolic Equations with Time-Space Dependent Diffusion Coefficients, Communications on Pure and Applied Analysis, 4 (2005), 241—266.

 

51.  G.-Q. Chen & M. Feldman: Potential Theory for Shock Reflection by a Large-Angle Wedge, Proceedings of the National Academy of Sciences USA (PNAS),  102 (2005), 15368—15372.

 

52.  G.-Q. Chen & H. Liu: Concentration and Cavitation in the Vanishing Pressure Limit of Solutions to the Euler Equations for Nonisentropic Fluids, Physica D: Nonlinear Phenomena, 189 (2004), 141—165.

 

53.  G.-Q. Chen & E.F. Toro: Centred Difference Schemes for Hyperbolic Equations, Journal of Hyperbolic Differential Equations, 1 (2004), 531—566.

 

54.  G.-Q. Chen & Y.-C. Li:  Stability of Riemann Solutions with Large Oscillation for the Relativistic Euler Equations, Journal of Differential Equations, 202 (2004), 332—353.

 

55.  G.-Q. Chen & Y.-C. Li:  Relativistic Euler Equations for Isentropic Fluids: Stability of Riemann Solutions with Large Oscillation, Zeitschrift für angewandte Mathematik und Physik, 55 (2004), 903—926.

 

56.  G.-Q. Chen & M. Feldman: Free Boundary Problems and Transonic Shocks for the Euler Equations in Unbounded Domains, Annali della Scuola Normale Superiore di Pisa (Classe di Scienze) (5), 3 (2004), 827—869.

 

57.  G.-Q. Chen & M. Feldman: Steady Transonic Shocks and Free Boundary Problems for the Euler Equations in Infinite Cylinders, Communications on Pure and Applied Mathematics, 57 (2004), 310—355.

 

58.  G.-Q. Chen & P. LeFloch: Existence Theory for the Isentropic Euler Equations, Archive for Rational Mechanics and Analysis, 166 (2003), 81—98.

 

59.  G.-Q. Chen & B. Perthame: Well-Posedness for Anisotropic Degenerate Parabolic-Hyperbolic Equations, Annales de l'Institut Henri Poincaré: Analyse Non Linéaire, 20 (2003), 645--668  (In memory of Ph. Bénilan).

 

60.  G.-Q. Chen & D. Wagner:  Global Existence of Weak Solutions to Exothermically Reacting and Compressible Euler Equations, Journal of Differential Equations, 191 (2003), 277—322.

 

61.  G.-Q. Chen & D. Wang: Existence and Continuous Dependence of Large Solutions for Magnetohydrodynamics, Zeitschrift für angewandte Mathematik und Physik, 54 (2003), 608—632.

 

62.  G.-Q. Chen & H. Frid:  Extended Divergence-Measure Fields and the Euler Equations of Gas Dynamics, Communications in Mathematical Physics, 236 (2003), 251—280.

 

63.  G.-Q. Chen, D. Hoff & K. Trivisa:  Global Solutions to a Model for Exothermically Reacting, Compressible Flows with Large Discontinuous Initial Data, Archive for Rational Mechanics and Analysis, 166 (2003), 321—358.    

 

64.  G.-Q. Chen & M. Feldman:  Multidimensional Transonic Shocks and Free Boundary Problems for Nonlinear Equations of Mixed Type, Journal of American Mathematical Society, 16 (2003), 461—494.

 

65.  G.-Q. Chen & H. Liu:  Formation of Delta-Shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Isentropic Euler Equations, SIAM Journal on Mathematical Analysis, 34 (2003), 925—938.

 

66.  G.-Q. Chen & B. Su:  A Viscous Approximation for a Multidimensional Unsteady Euler Flow: Existence Theorem for Potential Flow, Discrete and Continuous Dynamical Systems, 9 (2003), 1587—1606.

 

67.  G.-Q. Chen, B.-H. Li & T.-H. Li:  Entropy Solutions in L for the Euler Equations in Nonlinear Elastodynamics and Related Equations, Archive for Rational Mechanics and Analysis, 170 (2003), 331—357.

 

68.  G.-Q. Chen & T.-H. Li:  Global Entropy Solutions in L to the Euler Equations and  Euler-Poisson Equations for Isothermal Fluids with Spherical Symmetry, Methods and Applications of Analysis, 10 (2003), 215—244 (Invited paper).

 

69.  G.-Q. Chen & B. Su:  On Discontinuous Solutions for Hamilton-Jacobi Equations: Uniqueness and Regularity, Discrete and Continuous Dynamical Systems, 9 (2003), 167—192.

 

70.  G.-Q. Chen, H. Frid & Y. Li:  Uniqueness and Stability of Riemann Solutions with Large Oscillation in Gas Dynamics, Communications in Mathematical Physics, 228 (2002), 201—217.

 

71.  G.-Q. Chen & M. Krakta:  Global Solutions to the Compressible Navier-Stokes Equations with Spherical Symmetry and Free Boundary, Communications on Partial Differential Equations, 27 (2002), 907—944.

 

72.  G.-Q. Chen & D. Wang: Global Solutions of Nonlinear Magnetohydrodynamics with Large Initial Data, Journal of Differential Equations, 182 (2002), 344—376.

 

73.  G.-Q. Chen & H. Frid:  Uniqueness and Asymptotic Stability of Riemann Solutions for the Compressible Euler Equations, Transactions of the American Mathematical Society, 353 (2001), 1103—1117.

 

74.  G.-Q. Chen & P. LeFloch:  Entropies and Flux-Splittings for the Isentropic Euler Equations, Chinese Annals of Mathematics, 22B:2 (2001), 145—158 (Invited paper).

 

75.  G.-Q. Chen & P. Zhang:  On the Zero-Rossby Limit of the Primitive Equations of the Atmosphere, Nonlinearity, 14 (2001), 1279—1295 (In memory of Jacques-Louis Lions).

 

76.  G.-Q. Chen & E. DiBenedetto:  Stability of Entropy Solutions to the Cauchy Problem for a Class of  Hyperbolic-Parabolic Equations, SIAM Journal on Mathematical Analysis, 33 (2001), 751—762.

 

77.  G.-Q. Chen & P.-T. Kan:  Hyperbolic Conservation Laws with Umbilic Degeneracy II, Archive for Rational Mechanics and Analysis, 160 (2001), 325—354.

 

78.  G.-Q. Chen & P. LeFloch:  Compressible Euler Equations with General Pressure Law, Archive for Rational Mechanics and Analysis, 153 (2000), 221—259.

 

79.  G.-Q. Chen, T. Chang & S. Yang:  On the Riemann Problem for Two-Dimensional Euler Equations II: Interaction of Contact Discontinuities, Discrete and Continuous Dynamical Systems, 6 (2) (2000), 419—430.

 

80.  G.-Q. Chen & M. Rascle:  Initial Layers and Uniqueness of Weak Entropy Solutions to Hyperbolic Conservation Laws, Archive for Rational Mechanics and Analysis, 153 (2000), 205—220.

 

81.  G.-Q. Chen, D. Hoff & K. Trivisa:  Global Solutions of the Compressible Navier-Stokes Equations with Large Discontinuous Initial Data,   Communications on Partial Differential Equations, 25 (2000), 2233—2258.

 

82.  G.-Q. Chen:  Vacuum States and Global Stability of Rarefaction Waves for Compressible Flow, Methods and Applications of Analysis, 7 (2000), 337—362 (In honor of Cathleen S. Morawetz on her 77th birthday) (Invited paper).

 

83.  G.-Q. Chen & H. Frid:  Large-Time Behavior of Entropy Solutions of Conservation Laws, Journal of Differential Equations, 152 (1999), 308—357.

 

84.  G.-Q. Chen & H. Frid:  Decay of Entropy Solutions of Nonlinear Conservation Laws, Archive for Rational Mechanics and Analysis, 146(2) (1999), 95—127 (Dedicated to Peter D. Lax and Luis Nirenberg on their 70th Birthday).

 

85.  G.-Q. Chen & H. Frid:  Divergence Measure Fields and Hyperbolic Conservation Laws, Archive for Rational Mechanics and Analysis, 147 (1999), 89—118.

 

86.  G.-Q. Chen & D. Wang:  Formation of Singularities in Compressible Euler-Poisson Fluids with Heat Diffusion and Damping Relaxation, Journal of Differential Equations, 144 (1998), 44—65.

 

87.  G.-Q. Chen & H. Frid:  On the Compressible Euler Equations in Thermoelasticity, Matemática Contemporânea, 15 (1998), 67—86.

 

88.  G.-Q. Chen:  Remarks on Global Solutions to the Compressible Euler Equations with Spherical Symmetry, Proceedings of the Royal Society of Edinburgh, 127A (1997),  243—259.

 

89.  G.-Q. Chen & J.-G. Liu:  Convergence of Difference Schemes with High Resolution for Conservation Laws, Mathematics of Computation, 66 (1997), 1027—1053.

 

90.  G.-Q. Chen & H. Frid:  Asymptotic Stability of Riemann Waves for Conservation Laws, Zeitschrift für angewandte Mathematik und Physik, 48 (1997), 30—44.

 

91.  G.-Q. Chen:  Remarks on DiPerna's Paper ``Convergence of the Viscosity Method for Isentropic Gas Dynamics'', Proceedings of the American Mathematical Society, 125 (1997), 2981—2986.

 

92.  G.-Q. Chen & C.M. Dafermos:  Global Solutions in L for a System of Conservation Laws of Viscoelastic Materials with Memory, Journal of Partial Differential Equations, 10 (1997), 369—383.

 

93.  G.-Q. Chen & C.M. Dafermos:  The Vanishing Viscosity Method in One-Dimensional Thermoelasticity, Transactions of the American Mathematical Society, 347 (1995), 531—541.

 

94.  G.-Q. Chen & P.-T. Kan:  Hyperbolic Conservation Laws with Umbilic Degeneracy I, Archive for Rational Mechanics and Analysis, 130 (1995), 231—276.

 

95.  G.-Q. Chen & P. LeFloch: Entropy Flux-Splittings for Hyperbolic Conservation Laws, Communications on Pure and Applied Mathematics, 48 (1995), 691—729.

 

96.  G.-Q. Chen, T. Chang & S. Yang:  On the Riemann Problem for Two-Dimensional Euler Equations I: Interaction of Shocks and Rarefaction Waves, Discrete and Continuous Dynamical Systems, 1 (1995), 555—584.

 

97.  G.-Q. Chen, D. Levermore & T.-P. Liu:  Hyperbolic Conservation Laws with Stiff Relaxation Terms and Entropy, Communications on Pure and Applied Mathematics, 47 (1994), 787—830.

 

98.  G.-Q. Chen & J.-G. Liu:  Convergence of Second-Order Schemes for Isentropic Gas Dynamics, Mathematics of Computation, 6 (1993), 607—627.

 

99.  G.-Q. Chen & T.-P. Liu:  Zero Relaxation and Dissipation Limits for Hyperbolic Conservation Laws, Communications on Pure and Applied Mathematics, 46 (1993), 755—781.

 

100.                    G.-Q. Chen, Q. Du & E. Tadmor:  Spectral Viscosity Approximations to Multidimensional Scalar Conservation Laws, Mathematics of Computation, 6 (1993), 629—643.

 

101.                    G.-Q. Chen:  Global Solutions to the Compressible Navier-Stokes Equations for a Reacting Mixture, SIAM Journal on Mathematical Analysis, 23 (1992), 609—634.

 

102.                    G.-Q. Chen: The Method of Quasidecoupling for Discontinuous Solutions to Conservation Laws, Archive for Rational Mechanics and Analysis, 121 (1992), 131—185.

 

103.                    G.-Q. Chen:  Hyperbolic Systems of Conservation Laws with a Symmetry, Communications on Partial Differential Equations, 16 (1991), 1461—1487.

 

104.                    G.-Q. Chen & Y.-G. Lu:  Convergence of the Approximate Solutions to Isentropic Gas Dynamics, Acta Mathematica Scientia, 10 (1990), 39—45.

 

105.                    G.-Q. Chen & Y.-G. Lu:  A Study on the Method of Compensated Compactness, Chinese Science Bulletin, 9 (1988), 641—644 (in Chinese), 34 (1989), 15—19 (in English).

 

106.                    G.-Q. Chen & A. Rustichini:  The Riemann Solution to a System of Conservation Laws, with Application to a Non-Zero Sum Game, Contemporary Mathematics, 100 (1989), 287—298.

 

107.                    X. Ding, G.-Q. Chen & P. Luo:  Convergence of the Fractional Step Lax-Friedrichs Scheme and Godunov Scheme for Isentropic Gas Dynamics,   Communications in Mathematical Physics, 121 (1989), 63—84.

 

108.                    G.-Q. Chen:  Overtaking of Shocks of the Same Kind in the Isentropic Steady Supersonic Plane Flow, Acta Mathematica Scientia, 7 (1987), 311—327.

 

109.                    T. Chang & G.-Q. Chen:  Some fundamental Concepts about Systems of Two Spatial Dimensional Conservation Laws, Acta Mathematica Scientia, 6 (1986), 463—474.

 

110.                    T. Chang & G.-Q. Chen:  Diffraction of Planar Shock along the Compressive Corner, Acta Mathematica Scientia, 6 (1986), 241—257.

 

111.                    X. Ding, G.-Q. Chen & P. Luo:  Convergence of the Lax-Friedrichs Scheme for Isentropic Gas Dynamics (I), Acta Mathematica Scientia, 5 (1985), 415—432 (in English), 7 (1987), 467—480 (in Chinese);  (II), Acta Mathematica Scientia, 5 (1985), 433—472 (in English); 8 (1988), 61—94 (in Chinese).

 

112.                    G.-Q. Chen:  Convergence of the Lax-Friedrichs Scheme for Isentropic Gas Dynamics (III), Acta Mathematica Scientia, 6 (1986), 75—120 (in English); 8 (1988), 243—276 (in Chinese).

 

 

List of Invited Chapters/Survey Articles in Handbooks, Encyclopedias, Books, and Notices

 

 

1.      G.-Q. Chen: Tricomi Equation, In: Equations, Laws and Functions of Applied Mathematics, the Princeton Companion to Applied Mathematics, Princeton University Press, 2014 (arXiv:1311.3338).

 

2.      G.-Q. Chen: Gas Dynamics Equations: Computation, In: Encyclopedia of Applied and Computational Mathematics, Springer-Verlag: 2014.

 

3.      G.-Q. Chen & M. Feldman: Shock Reflection-Diffraction, von Neumann's Conjectures and Nonlinear Equations of Mixed Type, Proceedings of the 6th International Congress of Chinese Mathematicians, 2014 (arXiv:1311.5596).

 

4.      J.M. Ball & G.-Q. Chen:  Entropy and Convexity for Nonlinear Partial Differential Equations, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 371 (2013), no. 2005, 20120340.

 

5.      G.-Q. Chen, M. Slemrod & D. Wang:  Entropy, Elasticity, and the Isometric Embedding Problem: M3 àR6, In: Hyperbolic Conservation Laws and Related Analysis with Applications, pp. 95—112, Springer Proceedings in Mathematics and Statistics (PROMS), Eds. G.-Q. Chen, H. Holden, and K. Karlsen. Springer-Verlag: Berlin-Heidelberg, 2013.

 

6.      G.-Q. Chen & W. Xiang: Existence and Stability of Global Solutions of Shock Diffraction by Wedges for Potential Flow, In: Hyperbolic Conservation Laws and Related Analysis with Applications, pp. 113—142, Springer Proceedings in Mathematics and Statistics (PROMS), Eds. G.-Q. Chen, H. Holden, and K. Karlsen. Springer-Verlag: Berlin-Heidelberg, 2013 (with Wei Xiang).

 

7.      G.-Q. Chen: Multidimensional Conservation Laws: Overview, Problems, and Perspective, In: Nonlinear Conservation Laws and Applications, IMA Mathematics and Its Applications, Vol. 153, pp. 23—72,  Eds. A. Bressan, G.-Q. Chen, M. Lewicka & D. Wang, Springer-Verlag: New York, 2011.

 

8.      G.-Q. Chen, M. Slemrod & D. Wang: Transonic Flows and Isometric Embeddings, In: Nonlinear Conservation Laws and Applications, pp. 257—266,  IMA Volume in Mathematics and Its Applications 153,  Eds. A. Bressan, G.-Q. Chen, M. Lewicka & D.-H. Wang, Springer-Verlag: New York, 2011.

 

9.      G.-Q. Chen:  On Degenerate Partial Differential Equations, In: Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena, Eds. H. Holden and K.H. Karlsen, Contemporary Mathematics, 526, pp. 53—90, AMS: Providence, RI, 2010.

 

10.  G.-Q. Chen & M. Feldman:  Shock Reflection-Diffraction and Multidimensional Conservation Laws, In: Hyperbolic Problems: Theory, Numerics, and Applications, Eds. E. Tadmor, J.-G. Liu, and A. Tzavaras, Proc. Sympos. Appl. Math. 67, pp. 25—51, AMS: Providence, RI, 2010.

 

11.  G.-Q. Chen & B. Perthame: What Is a Kinetic Solution for Degenerate Parabolic-Hyperbolic Equations?  In: Notices of the American Mathematical Society, June/July Issue, pp. 737—739, 2010.

 

12.  G.-Q. Chen: Compressible Flows: Mathematical Theory, In: Encyclopedia of Mathematical Physics, Eds. J.-P. Francoise, G. Naber, and T.S. Tsun, Elsevier Limited: Oxford, UK, 2006.

 

13.  G.-Q. Chen: Euler Equations and Related Hyperbolic Conservation Laws, Chapter 1, Handbook of Differential Equations: Evolutionary Differential Equations, Vol.  2, pp. 1—104,  Eds. C.M. Dafermos and E. Feireisl,  Elsevier Science B.V: Amsterdam, The Netherlands, 2005.

 

14.  G.-Q. Chen: Some Recent Methods for Partial Differential Equations of Divergence Form,  Boletim da Sociedade Brasileira de Matemática (Bol. Soc. Bras. Math.), New Series, 34 (1) (2003), 107—144 (Invited paper)  (To IMPA on the Occasion of Its 50th Anniversary).

 

15.  G.-Q. Chen: Concentration in Solutions to Hyperbolic Conservation Laws, Contemporary Mathematics, 327 (2003), 41—60.

 

16.  G.-Q. Chen & D. Wang: The Cauchy Problem for the Euler Equations for Compressible Fluids, Chapter 5, Handbook of Mathematical Fluid Dynamics,  Vol. 1, pp. 421—543 , Eds. S. Friedlander and D. Serre, Elsevier Science B.V: Amsterdam, The Netherlands, 2002.

 

17.  G.-Q. Chen & H. Frid: On the Theory of Divergence-Measure Fields and Its Applications, Boletim da Sociedade Brasileira de Matemática  (Bol. Soc. Bras. Math.), 32 (2001), 1—33.

 

18.  G.-Q. Chen: Limit Behavior of Approximate Solutions to Conservation Laws, In: Multidimensional Hyperbolic Problems and Computations, edited  by J. Glimm and A. Majda, IMA Vol. 23,  38—57,  1991.

 

 

List of Main Conference Proceedings Papers, Announcement Papers, etc.

 

 

1.      G.-Q. Chen, M Slemrod & D. Wang: Mixed Type Problems for Transonic Flow in Gas Dynamics and Isometric Embedding in Geometry, In: Hyperbolic Problems—Theory, Numerics and Applications. Volume 1, 148–159, Ser. Contemp. Appl. Math. CAM, 17, World Sci. Publishing, Singapore, 2012.

 

2.      G.-Q. Chen & M. Feldman:  Shock Reflection-Diffraction and Nonlinear Partial Differential Equations of Mixed Type, In: Complex Analysis and Dynamical Systems IV, Contemporary Mathematics, vol. 554, Amer. Math. Soc., Providence, RI, 2011, pp. 55—72.

 

3.      G.-Q. Chen & M. Feldman: Shock Reflection-Diffraction and Multidimensional Conservation Laws, In: Hyperbolic Problems: Theory, Numerics, and Applications, Eds. E. Tadmor, J.-G. Liu & A. Tzavaras, Proc. Sympos. Appl. Math.  67, pp. 25—51, AMS: Providence, RI, 2010.

 

4.      G.-Q. Chen, M. Slemrod & D. Wang: Conservation Laws: Transonic Flow and Differential Geometry, In: Hyperbolic Problems: Theory, Numerics, and Applications, Eds. E. Tadmor, J.-G. Liu, and A. Tzavaras, Proc. Sympos. Appl. Math. 67, pp. 218—226,  AMS: Providence, RI, 2010.

 

5.      G.-Q. Chen, M. Slemrod & D. Wang: A Fluid Dynamic Formulation of the Isometric Embedding Problem in Differential Geometry (Dedicated to Walter Strauss on the occasion of his 70th birthday), Quarterly of Applied Mathematics, 68 (2010), 73—80.

 

6.      G.-Q. Chen: Some Problems in the Theory of Multidimensional Hyperbolic Conservation Laws, In: Hyperbolic Problems: Theory, Numerics, and Applications, pp. 85—94, Yokohama Publishers: Yokohama, Japan, 2006.

 

7.      A. Chen, G.-Q. Chen & R.A. Freeman: Conditional Gain Is Necessary and Sufficient for the Robust Stabilization of Nonlinear Systems, In: Proceedings of the 43rd IEEE Conference on Decision and Contro}, December 14—17,  2004, Atlantis, Paradise Island, Bahamas.    http://ieeexplore.ieee.org/iel5/9774/30842/01430230.pdf

 

8.      G.-Q. Chen & K. Trvisia: Analysis on Models for Exothermically Reacting, Compressible Flows With Large Discontinuous Initial Data, In: Nonlinear Partial Differential Equations and Related Analysis, Eds. G.-Q. Chen, G. Gasper, and J. Jerome, Contemporary Mathematics, 371, pp. 73—92, AMS: Providence, 2005.

 

9.      G.-Q. Chen & M. Feldman: Existence and Stability of Multidimensional Transonic Shocks for the Euler Equations for Steady Potential Fluids in Unbounded Domains, In: Hyperbolic Problems: Theory, Numerics, Applications (Proceedings of the 9th International Conference on Hyperbolic Problems, CalTech, Pasadena, March 25—29, 2002),  Eds. T.Y. Hou and E. Tadmor, pp. 419—432, Springer-Verlag:  Berlin-Heidelberg-New York, 2003.

 

10.  G.-Q. Chen, D. Hoff & K. Trivisa: Analysis on a Model for the Dynamic Combustion of a Compressible, Reacting Fluid, In: Hyperbolic Problems: Theory, Numerics, and Applications (Proceedings of the 9th International Conference on Hyperbolic Problems, CalTech, Pasadena, March 25—29, 2002),  Eds. T.Y. Hou and E. Tadmor, pp. 433—442, Springer-Verlag: Berlin-Heidelberg-New York, 2003.

 

11.  G.-Q. Chen & B. Su: On Global Discontinuous Solutions for Hamilton-Jacobi Equations, C. R. Acad. Sci. Paris, Ser. I. 334 (2002), 113—118.

 

12.  G.-Q. Chen: Discontinuous Solutions to Nonlinear Evolutionary Partial Differential Equations, AMS/IP Studies in Advanced Mathematics, 20 (2001), 443—454.

 

13.  G.-Q. Chen: Compactness Methods and Hyperbolic Conservation Laws, AMS/IP Studies in Advanced Mathematics, 15 (2000), 34—75, AMS: Providence, RI; International Press: Cambridge, MA.

 

14.  G.-Q. Chen: Compactness and Asymptotic Behavior of Entropy Solutions without Locally Bounded Variation for Hyperbolic Conservation Laws, In: Hyperbolic Problems: Theory, Numerics, Applications     (Proceedings of the 7th International Conference, Zürich, February 1998),  International Series of Numerical Mathematics, Vol. 129,  pp. 139—148, Birkhäuser Verlag: Basel, Switzerland, 1999.

 

15.  G.-Q. Chen & H. Frid: Large-Time Behavior of Entropy Solutions for Multidimensional Conservation Laws, In: Advances in Nonlinear Partial Differential Equations and Related Areas, Eds. G.-Q. Chen et al,  pp. 28—44, World Scientific: Singapore, 1998.

 

16.  G.-Q. Chen & P. LeFloch: Entropies and Weak Solutions of the Compressible Isentropic Euler    Equations, C. R. Acad. Sci. Paris, Série I, 324, 1105—1110 (1997).

 

17.  G.-Q. Chen: Euler-Poisson-Darboux Equations and Hyperbolic Conservation Laws, In: Nonlinear Evolutionary Partial Differential Equations,  pp. 11—25, AMS/IP Studies in Advanced Mathematics, Vol. 3,  Eds. X. Ding & T.-P. Liu, International Press, Cambridge, Massachusetts, 1997.

 

18.  G.-Q. Chen & H. Frid: Asymptotic Decay of Solutions of Conservation Laws, C. R. Acad. Sci. Paris, Série I,  323 (1996), 257—262.

 

19.  G.-Q. Chen: Relaxation Limit for Conservation Laws, Z. Angew. Math. Mech. (ZAMM), Berlin 76, Suppl. 2, 381—384, 1996 (Proceedings of the ICIAM/GAMM 95—Hamburg, Applied Analysis, Eds. O. Mahrenholtz and R. Mennicken).

 

20.  G.-Q. Chen & P.-T. Kan: Global Solutions to Hyperbolic Conservation Laws with Umbilic Degeneracy, Proceedings of the 5th International Conferences on Hyperbolic Problems: Theory, Computation, and Application, J. Glimm, M.J. Graham, J.W. Grove & B.J. Plohr (eds.), pp. 368—374,  World Scientific Publishing Co. Pte. Ltd,  River Edge, New Jersey, 1996.

 

21.  G.-Q. Chen: Some Singular Limit Problems in Conservation Laws, Matemática Contemporânea, 8 (1995), 107—128.

 

22.  G.-Q. Chen & D. Wagner: Global Weak Solutions to Reacting Euler Equations, In: Nonlinear Hyperbolic Problems: Theoretical, Applied, and  Computational Aspects, Eds. A. Donato and F. Oliveri, Notes on Numerical Fluid Mechanics, Vol. 43, 144—149, Vieweg, Braunschweig, 1993.

 

23.  G.-Q. Chen & P. LeFloch: Entropy Flux-Splittings for Hyperbolic Conservation Laws, C. R. Acad. Sci. Paris, Série I, 317 (1993), 761—766.