[1] Bento M C, Bertolami O, Sen A. Generalized Chaplygin gas, accelerated expansion, and dark-energy-matter unification. Physical Review D, 2002, 66:043507 [2] Bianchini S, Bressan A. Vanishing viscosity solutions of nonlinear hyperbolic systems. Ann of Math, 2005, 161(1):223-342 [3] Bianchini S, Caravenna L. SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension. Comm Math Phys, 2012, 313(1):1-33 [4] Bianchini S, Marconi E. On the concentration of entropy for scalar conservation laws. Discrete Contin Dyn Syst, 2016, 9B(1):73-88 [5] Bianchini S, Modena S. On a quadratic functional for scalar conservation laws. J Hyperbolic Differ Equ, 2014, 11(2):355-435 [6] Bianchini S, Modena S. Quadratic interaction functional for general systems of conservation laws. Comm Math Phys, 2015, 338:1075-1052 [7] Brenier Y. Solutions with concentration to the Riemann problem for the one-dimensional Chaplygin gas equations. J Math Fluid Mech, 2005, 7:326-331 [8] Bressan A, Crasta G, Piccoli B. Well-posedness of the Cauchy problem for n×n systems of conservation laws. Mem Amer Math Soc, 2000, 146(694):viii+134 [9] Bressan A, Liu T P, Yang T. L1 stability estimates for n×n conservation laws. Arch Ration Mech Anal, 1999, 149(1):1-22 [10] Chen G Q. The Method of Quasi-Decoupling for Discontinuous Solutions to Conservation Laws. Arch Ration Mech Anal, 1992, 121(2):131-185 [11] Chen G Q, LeFloch P. Compressible Euler equations with general pressure law. Arch Ration Mech Anal, 2000, 3(153):221-259 [12] Chen G Q. Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (Ⅲ). Acta Mathematica Scientia, 1986, 6B(1):75-120 [13] Courant R, Friedrichs K O. Supersonic flow and shock waves. New York:Springer-Verlag, 1976 [14] Ding X Q, Chen G Q, Luo P Z. Convergence of the lax-friedrichs scheme for isentropic gas dynamics (I). Acta Mathematica Scientia, 1985, 5B(4):415-432 [15] Ding X Q, Chen G Q, Luo P Z. Convergence of the lax-friedrichs scheme for isentropic gas dynamics (Ⅱ). Acta Mathematica Scientia, 1985, 5B(4):433-472 [16] DiPerna R J. Convergence of the viscosity method for isentropic gas dynamics. Comm Math Phys, 1983, 91(1):1-30 [17] E W N, Robert V K. The initial-value problem for measure-valued solutions of a canonical 2×2 system with linearly degenerate fields. Comm Pure Appl Math, 199144(8/9):981-1000 [18] Guo L H, Sheng W C, Zhang T. The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system. Commun Pure Appl Anal, 2010, 9(2):431-458 [19] Huang F M, Wang Z. Well posedness for pressureless flow. Comm Math Phys, 2001, 222(1):117-146 [20] Huang F M, Wang Z. Convergence of Viscosity Solutions for Isothermal Gas Dynamics. SIAM J Math Anal, 2002, 34(3):595-610 [21] Keyfitz B L, Kranzer H C. A system of non-strictly hyperbolic conservation laws arising in elasticity theory. Arch Ration Mech Anal, 1980, 72(3):219-241 [22] LeFloch P G, Shelukhin V. Symmetries and global solvability of the isothermal gas dynamics equations. Arch Ration Mech Anal, 2005, 175(3):389-430 [23] Li T T, Zhou Y, Kong D X. Weak linear degeneracy and global classical solutions for general quasilinear hyperbolic systems. Comm Partial Differential Equations, 1994, 19(7/8):1263-1317 [24] Lions P L, Perthame B, Souganidis P E. Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Comm Pure Appl Math, 1996, 49(6):599-638 [25] Lions P L, Perthame B, Tadmor E. Kinetic formulation of the isentropic gas dynamics and p-systems. Comm Math Phys, 1994, 163(2):415-431 [26] Marconi E. Regularity estimates for scalar conservation laws in one space dimension. J Hyperbolic Differ Equ, 2018, 15(4):623-691 [27] Nishida T. Global solution for an initial boundary value problem of a quasilinear hyperbolic system. Proc Japan Acad, 1968, 44:642-646 [28] Peng Y J. Explicit solutions for 2×2 linearly degenerate systems. Appl Math Lett, 1998, 11(5):75-78 [29] Serre D. Nonlinear oscillations of hyperbolic systems:methods and qualitative results. Ann Inst H Poincaré Anal Non Linéaire, 1991, 8(3/4):351-417 [30] Serre D. Richness and the classification of quasilinear hyperbolic systems//Multidimensional Hyperbolic Problems and Computations, Mineapolis, MN, 1989; IMA Vol Math Appl, Vol 29. New York:Springer, 1991:315-333 [31] Smoller J. Shock waves and reaction-diffusion equations. New York:Springer-Verlag, 1994 [32] Wagner D H. Equivalence of the Euler and Lagrangian Equations of Gas-dynamics for Weak Solutions. J Differential Equations, 1987, 68(1):118-136 [33] Zhou M Q. Real Analysis (in Chinese), 1st Ed. Beijing:Peking University Press, 2003 [34] Zhou Y. Low regularity solutions for linearly degenerate hyperbolic systems. Nonlinear Anal, 199626(11):1843-1857 |