JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (4): 55-65.doi: 10.6040/j.issn.1671-9352.0.2021.228
JIA Yi-fei, GUO Li-hui*, BAI Yin-song
CLC Number:
[1] GUO Lihui, SHENG Wancheng, ZHANG Tong. The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system[J]. Communications on Pure and Applied Analysis, 2010, 9(2):431-458. [2] KORCHINSKI D J. Solution of a Riemann problem for a 2×2 system of conservation laws possessing no classical weak solution[D]. New York: Adelphi University, 1977. [3] KEYFITZ B L, KRANZER H C. A viscosity approximation to a system of conservation laws with no classical Riemann solution[J]. Nonlinear Hyperbolic Problems: Lecture Notes in Mathematics, 1989, 1402:185-197. [4] KEYFITZ B L, KRANZER H C. Spaces of weighted measures for conservation laws with singular shock solutions[J]. Journal of Differential Equations, 1995, 118(2):420-451. [5] KRANZER H C, KEYFITZ B L.A strictly hyperbolic system of conservation laws admitting singular shocks[J]. Nonlinear Evolution Equations that Change Type: IMA Volumes in Mathematics and its Applications, 1990, 27:107-125. [6] TAN Dechun, ZHANG Tong, ZHENG Yuxi. Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws[J]. Journal of Differential Equations, 1994, 112(1):1-32. [7] CHENG Hongjun, YANG Hanchun. Delta shock waves in chromatography equations[J]. Journal of Mathematical Analysis and Applications, 2011, 380(2):475-485. [8] MITROVIC D, NEDELJKOV M. Delta shock waves as a limit of shock waves[J]. Journal of Hyperbolic Differential Equations, 2007, 4(4):629-653. [9] SHEN Chun. The Riemann problem for the Chaplygin gas equations with a source term[J]. Zeitschrift für Angewandte Mathematik und Mechanik, 2016, 96(6):681-695. [10] SHEN Chun. Delta shock wave solution for a symmetric Keyfitz-Kranzer system[J]. Applied Mathematics Letters, 2018, 77:35-43. [11] SHEN Chun.The multiplication of distributions in the one-dimensional Eulerian droplet model[J/OL]. Applied Mathematics Letters, 2021[2021-03-10]. https://doi.org/10.1016/j.aml.2020.106796. [12] SUN Meina. The multiplication of distributions in the study of delta shock wave for the nonlinear chromatography system[J]. Applied Mathematics Letters, 2019, 96:61-68. [13] SUN Meina. The singular solutions to a nonsymmetric system of Keyfitz-Kranzer type with initial data of Riemann type[J]. Mathematical Methods in the Applied Sciences, 2020, 43(2):682-697. [14] SUN Meina. Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state[J]. Nonlinear Analysis: Real World Applications, 2020, 53:103068. [15] ZHANG Yu, YANG Hanchun. Flux-approximation limits of solutions to the relativistic Euler equations for polytropic gas[J]. Journal of Mathematical Analysis and Applications, 2016, 435(2):1160-1182. [16] NEDELJKOV M. Shadow waves: entropies and interactions for delta and singular shocks[J]. Archive for Rational Mechanics and Analysis, 2010, 197(2):489-537. [17] DAW D A E, NEDELJKOV M. Shadow waves for pressureless gas balance laws[J]. Applied Mathematics Letters, 2016, 57:54-59. [18] DEDOVIC N, NEDELJKOV M. Delta shocks interactions and the wave front tracking method[J]. Journal of Mathematical Analysis and Applications, 2013, 403(2):580-598. [19] NEDELJKOV M. Higher order shadow waves and delta shock blow up in the Chaplygin gas[J]. Journal of Differential Equations, 2014, 256(11):3859-3887. [20] NEDELJKOV M. Split delta shocks: an overview[J]. Functional Analysis, Approximation and Computation, 2016, 8(1):61-77. [21] NEDELJKOV M, NEUMANN L, CBERGUGGENBERGER M, et al. Radially symmetric shadow wave solutions to the system of pressureless gas dynamics in arbitrary dimensions[J]. Nonlinear Analysis: Theory, Methods & Applications, 2017, 163:104-126. [22] NEDELJKOV M, RUŽICIC S. On the uniqueness of solution to generalized Chaplygin gas[J]. Discrete and Continuous Dynamical Systems. Series A, 2017, 37(8):4439-4460. [23] RUŽICIC S, NEDELJKOV M. Shadow wave tracking procedure and initial data problem for pressureless gas model[J]. Acta Applicandae Mathematicae, 2021, 171:10. [24] SUN Meina. Shadow wave solution for the generalized Langmuir isotherm in chromatography[J]. Archiv der Mathematik, 2016, 107(6):645-658. [25] CHENG Hongjun, YANG Hanchun. Riemann problem for the isentropic relativistic Chaplygin Euler equations[J]. Zeitschrift für Angewandte Mathematik und Physik, 2012, 63(3):429-440. |
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