Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 17, 2022
|
|
---|---|---|
Article Number | 10 | |
Number of page(s) | 25 | |
DOI | https://doi.org/10.1051/mmnp/2022009 | |
Published online | 20 May 2022 |
- M.C. Bento, O. Bertolami and A.A. Sen, Generalized Chaplygin gas, accelerated expansion, and dark-energy-matter unification. Phys. Rev. D 66 (2002) 043507. [CrossRef] [Google Scholar]
- M.C. Bento, O. Bertolami and A.A. Sen, Generalized Chaplygin gas and cosmic microwave background radiation constraints. Phys. Rev. D 67 (2003) 063003. [CrossRef] [Google Scholar]
- Y. Brenier and E. Grenier, Sticky particles and scalar conservation laws. SIAM J. Numer. Anal. 35 (1998) 2317–2328. [CrossRef] [MathSciNet] [Google Scholar]
- T. Chang, G. Chen and S. Yang, 2-D Riemann problem in gas dynamics and formation of spiral, in: Nonlinear Problems in Engineering and Science—Numerical and Analytical Approach (Beijing, 1991), Science Press, Beijing (1992), pp. 167–179. [Google Scholar]
- T. Chang, G. Chen and S. Yang, On the Riemann problem for two-dimensional Euler equations. I. Interaction of shocks and rarefaction waves. Discrete Contin. Dyn. Syst. 1 (1995) 555–584. [CrossRef] [Google Scholar]
- T. Chang, G. Chen and S. Yang, On the Riemann problem for two-dimensional Euler equations. II. Interaction of contact discontinuities. Discrete Contin. Dyn. Syst. 6 (2000) 419–430. [CrossRef] [Google Scholar]
- S. Chaplygin, On gas jets. Sci. Mem. Moscow Univ. Math. Phys. 21 (1904) 1–121. [Google Scholar]
- G. Chen and H. Liu, Formation of delta-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. SIAM J. Math. Anal. 34 (2003) 925–938. [CrossRef] [MathSciNet] [Google Scholar]
- G. Chen and H. Liu, Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids. Physica D 189 (2004) 141–165. [CrossRef] [MathSciNet] [Google Scholar]
- C.M. Dafermos, Hyperbolic Conversation Laws in Continuum Physics. Grundlehren der mathematischen Wissenchaften, Springer, Berlin-Heidelberg-New York (2010). [CrossRef] [Google Scholar]
- Q. Ding and L. Guo, The vanishing pressure limit of Riemann solutions to the non-isentropic Euler equations for generalized Chaplygin gas. Adv. Math. Phys. 2019 (2019) 1–12. [CrossRef] [Google Scholar]
- L. Guo, W. Sheng and T. Zhang, The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system. Commun. Pure Appl. Anal. 9 (2010) 431–458. [CrossRef] [MathSciNet] [Google Scholar]
- J. Hu, One-dimensional Riemann problem for equations of constant pressure fluid dynamics with measure solutions by viscosity method. Acta Appl. Math. 55 (1999) 209–229. [CrossRef] [MathSciNet] [Google Scholar]
- G. Jiang and E. Tadmor, Non-oscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19 (1998) 1892–1917. [CrossRef] [MathSciNet] [Google Scholar]
- H. Li and Z. Shao, Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas. Commun. Pure Appl. Anal. 15 (2016) 2373–2400. [CrossRef] [MathSciNet] [Google Scholar]
- J. Li, Note on the compressible Euler equations with zero temperature. Appl. Math. Lett. 14 (2001) 519–523. [CrossRef] [MathSciNet] [Google Scholar]
- M. Lin and L. Guo, The limit Riemann solutions to nonisentropic Chaplygin Euler equations. Open Math. 18 (2020) 1771–1787. [CrossRef] [MathSciNet] [Google Scholar]
- L. Pan and X. Han, The Aw-Rascle traffic model with Chaplygin pressure. J. Math. Anal. Appl. 401 (2013) 379–387. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Pang, Delta shock wave with Dirac delta function in multiple components for the system of generalized Chaplygin gas dynamics. Boundary Value Probl. 2016 (2016) 202. [CrossRef] [Google Scholar]
- Y. Pang, Delta shock wave in the compressible Euler equations for a Chaplygin gas. J. Math. Anal. Appl. 448 (2017) 245–261. [CrossRef] [MathSciNet] [Google Scholar]
- M.R. Setare, Interacting holographic generalized Chaplygin gas model. Phys. Lett. B 654 (2007) 1–6. [CrossRef] [Google Scholar]
- S.F. Shandarin and Ya.B. Zeldovich, The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium. Rev. Modern Phys. 61 (1989) 185–220. [CrossRef] [MathSciNet] [Google Scholar]
- C. Shen and M. Sun, Exact Riemann solutions for the drift-flux equations of two-phase flow under gravity. J. Differ. Equ. 314 (2022) 1–55. [CrossRef] [Google Scholar]
- W. Sheng, G. Wang and G. Yin, Delta wave and vacuum state for generalized Chaplygin gas dynamics system as pressure vanishes. Nonlinear Anal. 22 (2015) 115–128. [CrossRef] [Google Scholar]
- M. Sun, J. Xin, On the delta shock wave interactions for the isentropic Chaplygin gas system consisting of three scalar equations. Filomat 33 (2019) 5355–5373. [CrossRef] [MathSciNet] [Google Scholar]
- H. Tsien, Two dimensional subsonic flow of compressible fluids. J. Aeron. Sci. 6 (1939) 399–407. [CrossRef] [Google Scholar]
- T. von Karman, Compressibility effects in aerodynamics. J. Aeron. Sci. 8 (1941) 337–365. [CrossRef] [Google Scholar]
- G. Wang, The Riemann problem for one dimensional generalized Chaplygin gas dynamics. J. Math. Anal. Appl. 403 (2013) 434–450. [CrossRef] [MathSciNet] [Google Scholar]
- G. Yin and K. Song, Vanishing pressure limits of Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas. J. Math. Anal. Appl. 411 (2014) 506–521. [CrossRef] [MathSciNet] [Google Scholar]
- W.E. Yu, G. Rykov and Ya.G. Sinai, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics. Commun. Math. Phys. 177 (1996) 349–380. [CrossRef] [Google Scholar]
- Q. Zhang, The vanishing pressure limit of solutions to the simplified Euler equations for isentropic fluids. Ann. Appl. Math. 28 (2012) 115–126. [Google Scholar]
- 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) 593–630. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Zhang, Y. Pang and J. Wang, Concentration and cavitation in the vanishing pressure limit of solutions to the generalized Chaplygin Euler equations of compressible fluid flow. Eur. J. Mech. B-Fluids 78 (2019) 252–262. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Zhang and Y. Zhang, Interactions of delta shock waves for the equations of constant pressure fluid dynamics. Differ. Equ. Appl. 13 (2021) 63–84. [MathSciNet] [Google Scholar]
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