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[1] Agarwal R K, Halt D W. A modified CUSP scheme in wave/particle split form for unstructured grid Euler flows// Caughey D A, Hafes M M, eds. Frontiers of Computational Fluid Dynamics. John Wiley \& Sons, 1994
[2] F. Bouchut. On zero-pressure gas dynamics//Advances in Kinetic Theory and Computing. Ser Adv Math Appl Sci 22. River Edge, NJ: World Scientific, 1994: 171--190
[3] Brenier Y, Grenier E. Sticky particles and scalar conservation laws. SIAM J Numer Anal, 1998, 35: 2317--2328
[4] Chen G Q, Liu H. Formation of δ-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. SIAM J Math Anal, 2003, 34: 925--938
[5] Chen G Q, Liu H. Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids. Physica D, 2004, 189: 141--165
[6] Cheng H, Liu H, Yang H. Two-dimensional Riemann problem for zero-pressure gas dynamics with three constant states. J Math Anal Appl, 2008, 343: 127--140
[7] Courant R, Friedrichs K O. Supersonic Flow and Shock waves. New York: Interscience Publishers Inc, 1948
[8] E W, Rykov Yu G, Sinai Y G. Generalized varinational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics. Comm Math Phys, 1996, 177: 349--380
[9] J. Guckenheimer. Shocks and rarefactions in two space dimensions. Arch. Ration. Mech. Anal, 1975, 59: 281--291
[10] Huang F, Wang Z. Well posedness for pressureless flow. Comm Math Phys, 2001, 222: 117--146
[11] Li Y, Cao Y. Large partial difference method with second accuracy in gas dynamics. Sci Sinica A, 1985, 28: 1024--1035
[12] Li J, Li W. Riemann problem for the zero-pressure flow in gas dynamics. Progr Natur Sci, 2001, 5(11): 331--344
[12] Li J, Yang H. Delta-shock waves as limits of vanishing viscosity for multidimensional zero-pressure gas dynamics. Quart Appl Math, 2001, 59(2): 315--342
[13] Li J, Zhang T. Generalized Rankine-Hugoniot conditions of weighted Dirac delta waves of transportation equations//Chen G Q, eds. Nonlinear PDE and Related Areas. Singapore: World Scientific, 1998: 219--232
[14] Li J, Zhang T, Yang S. The Two-dimensional Riemann Prolem in Gas Dynamics. Pitman Monogr Surv Pure Appl Math 98. Longman Scientific and Technical, 1998
[15] Yu.G. Rykov. On the nonhamiltonian character of shocks in 2-D pressureless gas. Bollenttino U M I, 2002, 8(5-B): 55--78
[16] Shandarin S F, Zeldovich Y B. The large-scale structure of the universe: turbulence, intermittency, structure in a self-gravitating medium. Rev Mod Phys, 1989, 61: 185--220
[17] Sheng W. Two-dimensional Riemann problem for scalar conservation laws. J Differential Equations, 2002, 183: 239--261
[18] Sheng W, Zhang T. The Riemann problem for transportation equations in gas dynamics. Mem Amer Math Soc, 1999, 137(654)
[19] Sun W, Sheng W. Two dimensional non-selfsimilar initial value problem for adhesion partical dynamics. Appl Math Mech (Einglish Edition), 2007, 28(9): 1191--1198
[20] Sun W, Sheng W. The non-selfsimilar Riemann problem for 2-D zero-pressure in gas dynamics. Chin Ann Math, 2007, 28B(6): 701--708
[21] Tan D, Zhang T. Two dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws. (I) Four-J cases. J Differ Equ, 1994, 111(1): 203--254
[22] Tan D, Zhang T, Zheng Y. Delta-shock wave as limits of vanishing viscosity for hyperbolic system of conservation laws. J Differ Equ, 1994, 112(1): 1--32
[23] Wang Z, Ding X. Uniqueness of generalized solution for the Cauchy problem of transportation equations. Acta Math Sci, 1997, 17(3): 341--352
[24] Wang Z, Huang F, Ding X. On the Cauchy problem of transportation equations. Acta Math Appl Sinica, 1997, 13(2): 113--122
[25] Yang H. Riemann problem for a class of coupled hyperbolic system of conservation laws. J Differetial Equations, 1999, 159: 447--484
[27] Yang H. Generalized plane delta-shock waves for n-dimensional zero-pressure gas dynamics. J Math Anal Appl, 2001, 260: 18--35
[26] Yang H, Sun W. The Riemann problem with delta initial data for a class of coupled hyperbolic system of conservation laws. Nonlinear Analysis, 2007, 67: 3041--3049
[27] Zhang P, Zhang T. Generalized characteristic analysis and Guckenheimer structure. J Differ Equ, 1999, 152: 409--430
[28] Zheng Y. Systems of Conservation Laws: Two-Dimensional Riemann Problems. Progress in Nonlinear Differential Equations and Their
Applications 38. Boston: Birkäuser, 2001
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