Construction and qualitative behavior of solutions for a system of nonlinear hyperbolic conservation laws with damping

Authors:
L. Hsiao and S. Q. Tang

Journal:
Quart. Appl. Math. **53** (1995), 487-505

MSC:
Primary 35L65; Secondary 35B40, 76L05, 76S05

DOI:
https://doi.org/10.1090/qam/1343463

MathSciNet review:
MR1343463

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References | Similar Articles | Additional Information

**[CH]**T. Chang and L. Hsiao,*The Riemann Problem and Interaction of Waves in Gas Dynamics*, Pitman Monographs and Surveys in Pure and Applied Mathematics**41**, Longman, 1989**[DD]**C. M. Dafermos and R. DiPerna,*The Riemann problem for certain classes of hyperbolic systems of conservation laws*, J. Diff. Eqs.**20**, 90-114 (1976)**[DH]**C. M. Dafermos and L. Hsiao,*Hyperbolic systems of balance laws with inhomogeneity and dissipation*, Indiana Univ. Math. J.**31**, 471-491 (1982)**[DCL]**X. X. Ding, G. Q. Chen, and P. Luo,*Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics*, Comm. Math. Phys.**121**, 63-84 (1989)**[HL]**L. Hsiao and Tai-ping Liu,*Convergence to Nonlinear Diffusion Waves for Solutions of a System of Hyperbolic Conservation Laws with Damping*, Comm. Math. Phys.**143**, 599-605 (1992)**[HM]**L. Hsiao and P. Marcati,*Nonhomogeneous Quasilinear Hyperbolic Systems Arising in Chemical Engineering*, Scuola Normale Superiore, Pisa, 1988, pp. 65-97**[HT]**L. Hsiao and S. Q. Tang,*Construction and qualitative behavior of solution of perturbed Riemann problem for the system of one-dimensional isentropic flow with damping*(accepted by J. Diff. Eqs.)**[LI]**Tai-ping Liu,*Existence and uniqueness theorems for Riemann problems*, Trans. Amer. Math. Soc.**213**, 375-382 (1975)**[LI]**Tai-ping Liu,*Quasilinear hyperbolic systems*, Comm. Math. Phys.**68**, 141-172 (1979)**[LT]**M. Luskin and B. Temple,*The existence of a global weak solution to the nonlinear waterhammer problem*, Comm. Pure Appl. Math.**35**, 697-735 (1982)**[LY]**Ta-tsien Li and Wen-ci Yu,*Boundary value problems for quasilinear hyperbolic systems*, Duke University Mathematics Series V, 1985**[LZ]**Ta-tsien Li and Yan-chun Zhao,*Global perturbation of the Riemann problem for the system of one-dimensional isentropic flow*, Lecture Notes in Mathematics 1306, Springer-Verlag, 1988, pp. 131-140**[SM]**J. Smoller,*Shock Waves and Reaction-Diffusion Equations*, Springer-Verlag, 1980**[TX]**S. Q. Tang and L. Xiao,*Global perturbation of the Riemann problem for the system of compressible flow through porous media*(I)**[TX]**S. Q. Tang and L. Xiao,*Global perturbation of the Riemann problem for the system of compressible flow through porous media*(II)**[YW]**Lung-An Ying and Ching-Hua Wang,*Global solutions of the Cauchy problem for a nonhomogeneous quasilinear hyperbolic system*, Comm. Pure Appl. Math.**33**, 579-597 (1980)

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Additional Information

DOI:
https://doi.org/10.1090/qam/1343463

Article copyright:
© Copyright 1995
American Mathematical Society