1 |
S. Albeverio and V. M. Shelkovich, On the delta-shock front, in: Analytical Approaches to Multidimensional Balance Laws (Ed. O.S.Rozanova), pp.45-88, Nova Science Publishers, 2006.
|
2 |
F. Bouchut, On zero pressure gas dynamics, in: Advances in kinetic theory and computing, 171-190, Ser. Adv. Math. Appl. Sci., 22, World Sci. Publ., River Edge, NJ, 1994.
|
3 |
A. Bressan, Hyperbolic Systems of Conservation Laws: The One-dimensional Cauchy Problem, Oxford Lecture Ser. Math. Appl., vol. 20, Oxford University Press, Oxford, 2000.
|
4 |
L. Guo, W. Sheng, and T. Zhang, The Two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system, Commun. Pure Appl. Anal. 9 (2010), no. 2, 431-458.
|
5 |
F. Huang and X. Yang, The two-dimensional Riemann problem for a class of systems of hyperbolic conservation law equations, Acta Math. Appl. Sinica 21 (1998), no. 2, 193-205.
|
6 |
W. Hwang and W. B. Lindquist, The 2-dimensional Riemann problem for a 2 2 hyperbolic law, (I) Isotropic media, SIAM J. Math. Anal. 34 (2002), no. 2, 341-358
DOI
ScienceOn
|
7 |
W. Hwang and W. B. Lindquist, The 2-dimensional Riemann problem for a 2 2 hyperbolic law, (II) Anisotropic media, SIAM J. Math. Anal. 34 (2002), no. 2, 359-384.
DOI
ScienceOn
|
8 |
G. Lai, W. Sheng, and Y. Zheng, Simple waves and pressure delta waves for a Chaplygin gas in multi-dimensions, Discrete Contin. Dyn. Syst. 31 (2011), no. 2, 489-523.
DOI
|
9 |
P. G. LeFloch, An existenceand uniqueness result for two nonstrictly hyperbolic systems, Nonlinear Evolution Equations that change Type, IMA Vol. Math. Appl. 27 ed B. Keyfitz and M. Shearer, Berlin, Springer, 107-125, 1990.
|
10 |
J. Li, T. Zhang, and S. Yang, The Two-Dimensional Riemann Problem in Gas Dynamics, Pitman Monographs and Surveys in Pure and Applied Mathematics, 98, Longman Scientific and Technical, 1998.
|
11 |
W. B. Lindquist, The scalar Riemann problem in two spatial dimensions: Piecewise smoothness of solutions and its breakdown, SIAM J. Math. Anal. 17 (1986), no. 5, 1178-1197.
DOI
|
12 |
W. B. Lindquist, Construction of solutions for two-dimensional Riemann problems, Comput. Math. Appl. Part A 12 (1986), no. 4-5, 615-630.
DOI
|
13 |
T. P. Liu and J. Smoller, On the vacuum state for isentropic gas dynamic equations, Adv. in Appl. Math. 1 (1980), no. 4, 345-359.
DOI
|
14 |
M. Nedeljkov, Shadow waves: entropies and interactions for delta and singular shocks, Arch. Ration. Mech. Anal. 197 (2010), no. 2, 487-537.
|
15 |
C. Shen and M. Sun, Interactions of delta shock waves for the transport equations with split delta functions, J. Math. Anal. Appl. 351 (2009), no 2, 747-755.
DOI
ScienceOn
|
16 |
M. Nedeljkov and M. Oberguggenberger, Interactions of delta shock waves in a strictly hyperbolic system of conservation laws, J. Math. Anal. Appl. 344 (2008), no. 2, 1143-1157.
DOI
ScienceOn
|
17 |
V. M. Shelkovich, Singular solutions of - and wave type of systems of conservation laws, and transport and concentration processes, Uspekhi Mat. Nauk 63 (2008), no. 3(381), 73-146; translation in Russian Math. Surveys 63 (2008), no. 3, 473-546.
|
18 |
C. Shen and M. Sun, Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model, J. Differential Equations 249 (2010), no. 12, 3024-3051.
DOI
ScienceOn
|
19 |
C. Shen, M. Sun, and Z. Wang, Global structure of Riemann solutions to a system of two-dimensional hyperbolic conservation laws, Nonlinear Anal. 74 (2011), no. 14, 4754-4770.
DOI
ScienceOn
|
20 |
W. Sheng and T. Zhang, The Riemann problem for the transportation equations in gas dynamics, Mem. Amer. Math. Soc. 137 (1999), no. 654, viii+77 pp.
|
21 |
W. Sun and W. Sheng, The non-selfsimilar Riemann problem for 2-D zero-pressure flow in gas dynamics, Chin. Ann. Math. Ser. B 28 (2007), no. 6, 701-708.
DOI
|
22 |
D. Tan and T. Zhang, Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws, (I): Four-J cases, J. Differential Equations 111 (1994), no. 2, 203-254.
DOI
ScienceOn
|
23 |
Y. Zheng, Systems of Conservation Laws, Birkhauser Verlag, 2001.
|
24 |
D. Tan and T. Zhang, Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws, (II): Initial data consists of some rarefaction, J. Differential Equations 111 (1994), no. 2, 255-283.
DOI
ScienceOn
|
25 |
D. Yoon and W. Hwang, Two-dimensional Riemann problem for Burgers equations, Bull. Korean Math. Soc. 45 (2008), no 1, 191-205.
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DOI
ScienceOn
|
26 |
T. Zhang and Y. Zheng, Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems, SIAM J. Math. Anal. 21 (1990), no. 3, 593-630.
DOI
|