Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Nonlinear diffusive phenomena of entropy weak solutions for a system of quasilinear hyperbolic conservation laws with damping


Authors: L. Hsiao and Tao Luo
Journal: Quart. Appl. Math. 56 (1998), 173-189
MSC: Primary 35L65; Secondary 35D99, 76N10
DOI: https://doi.org/10.1090/qam/1604829
MathSciNet review: MR1604829
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a system of isentropic flow through porous media and show that nonlinear diffusive phenomena occur even if there are shocks in the flow.


References [Enhancements On Off] (What's this?)

  • [CH] T. Chang and L. Hsiao, The Riemann Problem and Interaction of Waves in Gas Dynamics, Pitman Monographs and Surveys in Pure and Applied Math., vol. 41, Longman, 1989 MR 994414
  • [DD] C. M. Dafermos and R. DiPerna, The Riemann problem for certain classes of hyperbolic systems of conservation laws, J. Differential Equations 20, 90-114 (1976) MR 0404871
  • [DP] C. J. Van Duyn and L. A. Peletier, A class of similarity solutions of the nonlinear diffusion equation, Nonlinear Analysis 1, 223-233 (1977)
  • [HLI1] L. Hsiao and T. P. Liu, Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping, Comm. Math. Phys. 143, 599-605 (1992) MR 1145602
  • [HLI2] L. Hsiao and T. P. Liu, Nonlinear diffusive phenomena of nonlinear hyperbolic systems, Chinese Ann. Math. Ser. B 14, 465-480 (1993) MR 1254543
  • [HLU] L. Hsiao and T. Luo, Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media, J. Differential Equations 125, 329-365 (1996) MR 1378760
  • [HT1] L. Hsiao and S. Q. Tang, Construction and qualitative behavior of solutions for a system of nonlinear hyperbolic conservation laws with damping, Quart. Appl. Math. 53, 487-505 (1995) MR 1343463
  • [HT2] L. Hsiao and S. Q. Tang, Construction and qualitative behavior of the solution of the perturbated Riemann problem for the system of one-dimensional isentropic flow with damping, J. Differential Equations 123, 480-503 (1995) MR 1362883
  • [LI] Tai-ping Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc. 213, 375-382 (1975) MR 0380135
  • [SM] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1980 MR 1301779

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35L65, 35D99, 76N10

Retrieve articles in all journals with MSC: 35L65, 35D99, 76N10


Additional Information

DOI: https://doi.org/10.1090/qam/1604829
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society