Updated April 1, 2016
  1. Two-Dimensional Riemann Problem for a Single Conservation Law, (with Tong Zhang), Transactions of the American Mathematical Society, 312(1989), 589-619.
  2. Riemann Problem for Gasdynamic Combustion, (with Tong Zhang), Journal of Differential Equations, 77(1989), 203-230.
  3. Conjecture on Structure of Solutions of Riemann Problem for 2-D Gasdynamic Systems, (with Tong Zhang), SIAM Journal on Mathematical Analysis, 21(1990), 593-630.
  4. Concentration in a sequence of solutions to the nonlinear Klein-Gordon equation, Indiana University Mathematics Journal, 40(1991), 201-235.
  5. Concentration-Cancellation for the Velocity Fields of Two Dimensional Incompressible Fluid Flows, Communications in Mathematical Physics, 135 (1991), 581-594.
  6. Regularity of Weak Solutions to Two Dimensional Semicoupled Dirac-Klein-Gordon System, Commun. Math. Phys., 151(1993), 67-87.
  7. Delta-Shock Waves as Limits of Vanishing Viscosity for Hyperbolic Systems of Conservation Laws, (with Dechun Tan and Tong Zhang), Journal of Differential Equations, 112(1994), 1-32.
  8. Existence of Global Weak Solutions to One-Component Vlasov-Poisson and Fokker-Planck-Poisson Systems in One Space Dimension with Measures as Initial Data, (with Andrew Majda), Commu. Pure Appl. Math., XLVII(1994), 1365-1401.
  9. On a Nonlinear Hyperbolic Variational Equation: I. Global Existence of Weak Solutions, (with John Hunter), Arch. Rat. Mech. Anal., 129(1995), 305--353.
  10. On a Nonlinear Hyperbolic Variational Equation: II. The Zero Viscosity and Dispersion Limits, (with John Hunter), Arch. Rat. Mech. Anal., 129(1995), 355--383.
  11. Concentrations in the One-Dimensional Vlasov-Poisson Equations, I: Temporal Development and Non-unique Weak Solutions in the Single Component Case, (with Andrew Majda and George Majda), Physica D., 74(1994), 268-300.
  12. Concentrations in the One-Dimensional Vlasov-Poisson Equations, II: Screening and the Necessity for Measure-valued Solutions in the Two Component Case, (with Andrew Majda and George Majda), Physica D., 79(1994), 41-76.
  13. On a Completely Integrable Nonlinear Hyperbolic Variational Equation, (with John Hunter), Physica D., 79(1994), 361-386.
  14. Steady States of the Vlasov-Fokker-Planck System, (with Bob Glassey and Jack Schaeffer), J. Math. Anal. Appl., 202(1996), 1058--1075.
  15. Singularities of a Variational Wave Equation, (with Bob Glassey and John Hunter), Journal of Differential Equations, 129(1996), 49-78.
  16. Vlasov-Poisson Systems with Measures as Initial Data, (Exposition), Proceedings of the ICIAM/GAMM 95, Hamburg, ZAMM (Zeitschrift fur angewandte mathematik und mechan), 76(1996), Special issue 2, Applied Analysis, (Eds: Oskar Mahrenholts and Reinhard Mennicken), p. 109. Akademie Verlag 1996.
  17. Explicit and Exact Swirling Solutions of the 2-D Euler Equations, (with Tong Zhang), Proceedings of the ICIAM/GAMM 95, Hamburg, ZAMM(Zeitschrift fur angewandte mathematik und mechan), 76(1996), Special issue 2, Applied Analysis, (Eds: Oskar Mahrenholts and Reinhard Mennicken), p. 145. Akademie Verlag 1996.
  18. Exact Spiral Solutions of the Two Dimensional Euler Equations, (with Tong Zhang), Discrete and Continuous Dynamical Systems, 3(1997), 117--133. Abstract
  19. Singularities and Oscillations in a Nonlinear Variational Wave Equation, (with Bob Glassey and John Hunter), in Singularities and Oscillations (IMA Proceedings Volume 91, April 1995 Workshop), editors Jeffrey Rauch and Michael Taylor, pp 37-60. Springer-Verlag, 1997.
  20. Axisymmetric Solutions of the Euler Equations for Polytropic Gases, (with Tong Zhang), Arch. Rat. Mech. Anal. 142(1998), 253--279. Abstract
  21. Swirling Solutions of the Two-Dimensional Compressible Euler Equations, (with Tong Zhang), in Proceedings of the International Conference on Dynamical Systems and Differential Equations, (Conference held between May 29-June 1, 1996) editors Wenxiong Chen and Shouchuan Hu, Publisher Southwest Missouri State University, 1998, Vol. 2, pp.367--378.
  22. Existence of Solutions to the Transonic Pressure-Gradient Equations of the Compressible Euler Equations in Elliptic Regions, Communications in Partial Differential Equations, 22(1997), 1849--1868.
  23. Weak Solutions for the Equations of Incompressible and Inviscid Fluid Dynamics, with M. C. Lopes Filho and H. J. Nussenzveig Lopes, 22nd Brazilian Colloquium in Mathematics, Institute of Pure and Applied Mathematics, Rio de Janeiro, Brazil, 1999. 129pp.
  24. Systems of Conservation Laws with Incomplete Sets of Eigenvectors Everywhere, in book Advances in Nonlinear Partial Differential Equations and Related Areas, a volume in honour of Professor Xiaqi Ding, Editors Gui-Qiang Chen, Yanyan Li, Xiping Zhu, and Daomin Cao, World Scientific, Singapore, New Jersey, London, Hong Kong, 1998, pp.399--426. Abstract
  25. Convergence of the Vanishing Viscosity Approximation for Superpositions of Confined Eddies, (with Milton Lopes Filho and Helena Nussenzveig Lopes), Commun. Math. Phys., 201(1999), 291--304. Abstract
  26. On Oscillations of an Asymptotic Equation of a Nonlinear Variational Wave Equation, (with Ping Zhang), Asymptotic Analysis, 18(1998), 307--327. Abstract
  27. On the Existence and Uniqueness of Solutions to an Asymptotic Equation of a Variational Wave Equation, (with Ping Zhang), Acta Mathematica Sinica (English Series), 15(1999), 115-130. Abstract
    2000--2004
  28. Systems of Conservation Laws: Two-Dimensional Riemann Problems, 317pp., Birkhauser, 2001.
  29. Some Problems of Incompressible Fluid Dynamics, in book Some Current Topics on Nonlinear Conservation Laws: Lectures from the Morningside Center of Mathematics, 1. Ed. Ling Hsiao and Zhouping Xin. Volume 15 of the series AMS/IP Studies in Advanced Mathematics, copublished by the American Mathematical Society and the International Press, pp. 195--226, May 2000.
  30. Rarefactive Solutions to a Nonlinear Variational Wave Equation of Liquid Crystals, (with Ping Zhang), Commun. Partial Differential Equations, 26(2001), 381--419.
  31. The Young Measure Method for a Nonlinear Variational Wave Equation, (with Ping Zhang), Conference proceeding for the Conference at the Chinese University of Hong Kong: ``IMS Conference on Differential Equations from Mechanics'', May 31 -- June 4, 1999. Methods and Applications of Analysis, 8(2001), No. 4, 681--688.
  32. Existence and Uniqueness of Solutions to an Asymptotic Equation of a Variational Wave Equation with General Data, (with Ping Zhang), Arch. Rat. Mech. Anal., 155(2000), pp. 49--83. Abstract
  33. On the Second-Order Asymptotic Equation of a Variational Wave Equation, (with Ping Zhang), Proceedings of the Royal Society of Edinburgh, A. Mathematics, 132A (2002), 483--509
  34. Singular and Rarefactive Solutions to a Nonlinear Variational Wave Equation of Liquid Crystals, (with Ping Zhang), Chinese Annals of Math., 22B, 2(2001), 159--170.
  35. The Limit from the Schrodinger-Poisson to the Vlasov-Poisson Equations with General Data in One Dimension, (with Ping Zhang and N. Mauser), Comm. Pure Appl. Math., Vol. LV(2002), 582--632. Abstract
  36. Transient Analysis of Immigration Birth-Death Processes with Total Catastrophes, (with Xiuli Chao), Probability in the Engineering and Informational Sciences , 17(2003), 83--106. Cambridge University Press.
  37. Weak Solutions to a Nonlinear Variational Wave Equation, (with Ping Zhang), Arch. Rat. Mech. Anal., 166(2003), 303--319.
  38. A global solution to a two-dimensional Riemann problem involving shocks as free boundaries, Acta Mathematicae Applicatae Sinica (English series), 19(2003), 559--572.
  39. Effect of Solutes on Dislocation Motion -- A Phase-Field Simulation, (with S.Y. Hu, Y.L. Li, and L.Q. Chen) Abstract, International Journal of Plasticity , 20 (2004), 403--425.
  40. Transient analysis of linear birth-death processes with immigration and emigration, (with Xiuli Chao and Xiaomei Ji) Abstract, Probability in the Engineering and Informational Sciences , 18 (2004), 141--159.
    2005-- 2009
  41. Weak solutions to a nonlinear variational wave equation with general data, (with Ping Zhang), Ann. I. H. Poincar\'e, 22(2005) 207--226.
  42. On the global weak solutions to a variational wave equation, with Ping Zhang, book chapter in ``Handbook of Differential Equations, Volume 2: Evolutionary Equations.'' Editors Dafermos and Feireisl, Elsevier B.V, published in October of 2005.
  43. Numerical evidence of nonuniqueness in the evolution of vortex sheets, (with Milton Lopes-Filho, John Lowengrub, and Helena Lopes), ESAIM: M2AN, 40(2006), 225--237.
  44. Conservative Solutions to a Nonlinear Variational Wave Equation (with Alberto Bressan), Preprint in ps, Comm. Math. Phys., 266(2006), 471-497.
  45. Two-dimensional regular shock reflection for the pressure gradient system of conservation laws, Paper in pdf, Acta Mathematicae Applicatae Sinica Vol. 22 (2006), No. 2, pp. 177--210 (English series).
  46. Shock reflection for the Euler system, Paper in ps, Hyperbolic Problems Theory, Numerics and Applications (Proceedings of the Osaka meeting 2004). Ed. F. Asakura (Chief), H. Aiso, S. Kawashima, A. Matsumura, S. Nishibata, K. Nishihara; Yokohama Publishers (Japan), Vol. II (2006), pp.425--432.
  47. Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations, (with Jiequan Li and Tong Zhang), Comm. Math. Phys., Preprint in pdf, 267(2006), 1--12.
  48. Asymptotic Variational Wave Equations, (with Alberto Bressan and Ping Zhang), Preprint in pdf, Arch. Rat. Mech. Anal., 183(2007), 163-185.
  49. A Complete Global Solution to the Pressure Gradient Equation (with Zhen Lei) Preprint in ps , J. Differential Equations , 236 (2007), 280 -- 292.
  50. Interaction of Rarefaction Waves of the Two-Dimensional Self-Similar Euler Equations (with Jiequan Li) Preprint in pdf , Arch. Rat. Mech. Anal., 193(2009), 623--657.
  51. Transonic shock formation in a rarefaction Riemann problem for the 2-D compressible Euler equations, (author list is James Glimm, Xiaomei Ji, Jiequan Li, Xiaolin Li, Peng Zhang, Tong Zhang, and Yuxi Zheng), Preprint in pdf , SIAM: J. Applied Mathematics, 69(2008), 720--742.
  52. Absorption of Characteristics by Sonic Curves of the Two-Dimensional Euler Equations, dedicated to Professor Tatsien Li (Daqian Li) on his 70th birthday, Disc. Cont. Dyna. Syst., 23(2009), No.1/2, 605--616. Offprint in pdf.
  53. The Compressible Euler System in Two Space Dimensions, (Shanghai Summer School Lecture Notes, Summer 2007.) Preprint in pdf. in Series in Contemporary Applied Mathematics - Vol. 13, Jun 2009, NONLINEAR CONSERVATION LAWS, FLUID SYSTEMS AND RELATED TOPICS, edited by G.Q. Chen, Ta-Tsien Li & Chun Liu. World Scientific and the Higher Education Press, pp.301--.
  54. Semi-Hyperbolic Patches of Solutions of the Pressure Gradient System Preprint in ps . With Kyungwoo Song. Disc. Cont. Dyna. Syst., series A, 24(2009), 1365--1380.
    2010-- 2012
  55. The Interaction of Rarefaction Waves of the Two-Dimensional Euler Equations, with Xiao Chen, Indiana University Mathematics Journal, 59(2010), 231--256.
  56. Conservative solutions to a system of variational wave equations of nematic liquid crystals, with Ping Zhang, Arch. Rat. Mech. Anal., 195(2010), 701--727.
  57. Interaction of Four Rarefaction Waves in the Bi-Symmetric Class of the Two-Dimensional Euler Equations, with Jiequan Li, Comm. Math. Phys., 296(2010), 303-321.
  58. An Introduction to a Variational Wave Equation, book chapter,in Lectures on the Analysis of Nonlinear Partial Differential Equations, Vol. 1, in series Morningside Lectures in Mathematics, Eds Fanghua Lin, Xueping Wang, and Ping Zhang, Higher Education Press and International Press, 2009, pp.285--317.
  59. TWO-DIMENSIONAL RIEMANN PROBLEMS: FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS, (with Jiequan Li, Wancheng Sheng and Tong Zhang) a survey paper, Acta Mathematica Scientia, 29B(2009), 777-802. Offprint .
  60. Two-Dimensional Riemann Problems for Conservation Laws, Oberwolfach Workshop on Hyperbolic Conservation Laws, Organised by C. M. Dafermos, D. Kroner, R. J. LeVeque, Report No. 56/2008, pp. 55--58, Preprint in pdf .
  61. Two-Dimensional Riemann Problems for the Compressible Euler System, conference proceeding Preprint in pdf on the sixtieth birthday of Andy Majda. (January 2009). Chin. Ann. Math., Series B. 30B(6), 2009, 845--858.
  62. Characteristic Decompositions and Interactions of Rarefaction Waves of 2-D Euler Equations, With Zhicheng Yang, Jiequan Li, J. Differential Equations, 250(2011), 782--798.
  63. Semi-Hyperbolic Patches of Solutions of the Two-Dimensional Euler equations, with Mingjie Li, Arch. Rat. Mech. Anal, 201(2011), 1069--1096.
  64. The Pressure Gradient System, (with Zachary Robinson), Methods and Applications of Analysis, 17 ( 2010), 263--278.
  65. Simple waves and pressure delta waves for a Chaplygin gas in multi-dimensions, (with Geng Lai and Wancheng Sheng), Disc. Cont. Dyna. Syst., Series A, 31(2011), 489--523.
  66. Semi-hyperbolic waves in two-dimensional compressible Euler systems, in IMA Summer Program on Nonlinear Conservation Laws and Applications, summer 2009, Ed.: A. Bressan, G. Chen, M. Lewicka, and D. Wang, Springer-verlag 2011, pp. 501.
  67. Energy conservative solutions to a one-dimensional full variational wave system, (with Ping Zhang), Comm. Pure Appl. Math., 65(2012), 683-726.
  68. Local Existence of Classical Solutions to Shallow Water Equations with Cauchy Data Containing Vacuum (with Ben Duan and Zhen Luo), SIAM J. Math. Anal., 44 (2012), 541-567.
  69. A New Differential Operator Method to Study the Mechanical Vibration, with Quansheng Ji, Xiaomei Ji, Linhong Ji, Modern Mechanical Engineering, 2(2012), 65-70.
    New: (2013--)
  70. Singularity and existence to a wave system of nematic liquid crystals, with Geng Chen, J. Math. Anal. Appl., 398 (2013), 170-188.
  71. Energy Conservative Solutions to a Nonlinear Wave System of Nematic Liquid Crystals, with Ping Zhang and Geng Chen, Comm. Pure Appl. Anal., 12(2013), 1445-1468.
  72. Characteristic Decouplings and Interactions of Rarefaction Waves of 2-D Euler Equations, with Xiaomei Ji, J. Math. Anal. Appl., 406(2013), 4--14.
  73. The regularity of semi-hyperbolic patches near sonic lines for the pressure gradient equation in gas dynamics, with Qin Wang, Indiana U. Math. J., 63 (2014), no. 2, 385 -- 402.
  74. Sonic-supersonic solutions for the steady Euler equations, Indiana U. Math. J. 63 No. 6 (2014), 1785 -- 1817 with Tianyou Zhang.
  75. The regularity of semi-hyperbolic patches near sonic lines for the 2-D Euler system in gas dynamics, with Qin Wang, Kyungwoo Song, SIAM J. Math. Anal. (in press 3/26/2015)
  76. No blow-up to a variational wave equation in liquid crystals, with Jingchi Huang. J. Math. Phys. (in press).
  77. The Structure of Solutions Near a Sonic Line in Gas Dynamics via the Pressure Gradient Equation, with Tianyou Zhang, J. Math. Anal. Appl., in press (April 2016).
  78. The construction of inclusive supersonic-sonic solutions of the steady Euler system, with Joe Roberts, preprint 2016.


ARTICLES also available:

  1. Axisymmetric Solutions of the Euler Equations for Sub-Square Polytropic Gases, (with Tong Zhang), free distribution upon request. Abstract
  2. Axisymmetric Solutions of the Euler Equations for Super-Square Polytropic Gases, (with Tong Zhang), free distribution upon request. Abstract
  3. Shock Wave Solutions to the Axisymmetric Euler Equations for Polytropic Gases, free distribution upon request. Abstract


OTHER ARTICLES:

  1. Math Review: Featured review of ``Vorticity and Incompressible Flow, by Majda and Bertozzi'', preprint (text) galleyproof.pdf
  2. Biography of Professor Tong Zhang, (in Chinese), free distribution upon request.
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