Delta-shock for the nonhomogeneous pressureless Euler system

키워드

참고문헌 (34)

1. F. Bouchut, "On zero pressure gas dynamics, in Advances in Kinetic Theory and Computing", Adv. Math. Appl. Sci., 22, pp.171~190 (1994)[DOI]
2. Y. Brenier, "Sticky particles and scalar conservation laws", SIAM J. Numer. Anal, 35(6), pp.2317~2328 (1998)[DOI]
3. C. M. Dafermos, "Solution of the Riemann problem for a class of hyperbolic systems of conservation laws by the viscosity method", Arch. Rational Mech. Anal, 52, pp.1~9 (1973)[DOI]
4. V. G. Danilov, "Dynamics of propagation and interaction of δ-shock waves in conservation law systems", J. Differential Equations, 211(2), pp.333~381 (2005)[DOI]
5. R. De lacruz, "Riemann problem for a 2×2 hyperbolic system with linear damping", Acta Appl. Math, 170, pp.631~647 (2020)[DOI]
6. R. De la cruz, "Vanishing viscosity limit for Riemann solutions to a 2×2 hyperbolic system with linear damping", Asymptot. Anal, 3, pp.275~296 (2022)[DOI]
7. X. Q. Ding, "Existence and uniqueness of discontinuous solutions defined by Lebesgue-Stieltjes integral", Sci. China Ser. A, 39(8), pp.807~819 (1996)
8. F. Hou, "On the global existence and blowup of smooth solutions to the multidimensional compressible Euler equations with time-depending damping", Nonlinearity, 30(6), pp.2485~2517 (2017)[DOI]
9. J. Hu, "A limiting viscosity approach to Riemann solutions containing delta-shock waves for nonstrictly hyperbolic conservation laws", Quart. Appl. Math, 55(2), pp.361~373 (1997)[DOI]
10. H. C. Kranzer, "Nonlinear evolution equations that change type", pp.107~125 (1990), Springer
11. P. Le Floch, "Nonlinear evolution equations that change type", pp.126~138 (1990), Springer
12. S. Li, "Riemann solutions of the anti-Chaplygin pressure Aw-Rascle model with friction", J. Math. Phys, 63(12), pp.121509~ (2022)[DOI]
13. S. Li, "Delta shock wave as limits of vanishing viscosity for zero-pressure gas dynamics with energy conservation law", ZAMM Z. Angew. Math. Mech, 103(5), pp.e202100377~ (2023)
14. J. Li, "The two-dimensional Riemann problem in gas dynamics" (1998), Longman
15. X. Pan, "Global existence of solutions to 1-d Euler equations with time-dependent damping", Nonlinear Anal, 132, pp.327~336 (2016)[DOI]
16. E. Yu. Panov, "δ′-shock waves as a new type of solutions to systems of conservation laws", J. Differential Equations, 228(1), pp.49~86 (2006)[DOI]
17. P. L. Sachdev, "Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems", pp.2000, Chapman & Hall
18. A. Sen, "Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws", J. Math. Phys, 60(5), pp.051510~ (2019)[DOI]
19. A. Sen, "The limiting behavior of the Riemann solution to the isentropic Euler system for logarithmic equation of state with a source term", Math. Methods Appl. Sci, 44(8), pp.7207~7227 (2021)[DOI]
20. S. F. Shandarin, "The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium", Rev. Modern Phys, 61(2), pp.185~220 (1989)[DOI]
21. Z. -Q. Shao, "Delta shocks and vacuum states for the isentropic magnetogasdynamics equations for Chaplygin gas as pressure and magnetic field vanish", Anal. Math. Phys, 12(3), pp.85~ (2022)[DOI]
22. C. Shen, "The Riemann problem for the pressureless Euler system with the Coulomb-like friction term", IMA J. Appl. Math, 81(1), pp.76~99 (2016)[DOI]
23. C. Shen, "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(12), pp.3024~3051 (2010)[DOI]
24. W. Sheng, "The Riemann problem for the transportation equations in gas dynamics", Mem. Amer. Math. Soc, 137(654), pp.77~ (1999)[DOI]
25. T. C. Sideris, "Long time behavior of solutions to the 3D compressible Euler equations with damping", Comm. Partial Differential Equations, 28(3-4), pp.795~816 (2003)[DOI]
26. M. Sun, "Delta shock waves for the chromatography equations as self-similar viscosity limits", Quart. Appl. Math, 69(3), pp.425~443 (2011)[DOI]
27. M. Sun, "The exact Riemann solutions to the generalized Chaplygin gas equations with friction", Commun. Nonlinear Sci. Numer. Simul, 36, pp.342~353 (2016)[DOI]
28. D. C. Tan, "Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws. II. Initial data involving some rarefaction waves", J. Differential Equations, 111(2), pp.255~282 (1994)[DOI]
29. D. C. Tan, "Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws", J. Differential Equations, 112(1), pp.1~32 (1994)[DOI]
30. V. A. Tupchiev, "The method of introducing a viscosity in the study of a problem of decay of a discontinuity", Dokl. Akad. Nauk SSSR, 211, pp.55~58 (1973)
31. E. Weinan, "Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics", Comm. Math. Phys, 177(2), pp.349~380 (1996)
32. H. Yang, "Riemann problems for a class of coupled hyperbolic systems of conservation laws", J. Differential Equations, 159(2), pp.447~484 (1999)[DOI]
33. H. Yang, "New developments of delta shock waves and its applications in systems of conservation laws", J. Differential Equations, 252(11), pp.5951~5993 (2012)[DOI]
34. Y. Zhang, "The Riemann problem for the equations of constant pressure fluid dynamics with nonlinear damping", Int. J. Non-Lin. Mech, 133, pp.103712~ (2021)[DOI]

관련 논문AI추천