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.
- Tung Chang and Ling Hsiao, The Riemann problem and interaction of waves in gas dynamics, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 41, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. MR 994414
- C. M. Dafermos and R. J. DiPerna, The Riemann problem for certain classes of hyperbolic systems of conservation laws, J. Differential Equations 20 (1976), no. 1, 90–114. MR 404871, DOI https://doi.org/10.1016/0022-0396%2876%2990098-X
C. J. Van Duyn and L. A. Peletier, A class of similarity solutions of the nonlinear diffusion equation, Nonlinear Analysis 1, 223–233 (1977)
- Ling 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 (1992), no. 3, 599–605. MR 1145602
- Ling Hsiao and Tai-Ping Liu, Nonlinear diffusive phenomena of nonlinear hyperbolic systems, Chinese Ann. Math. Ser. B 14 (1993), no. 4, 465–480. A Chinese summary appears in Chinese Ann. Math. Ser. A 14 (1993), no. 6, 740. MR 1254543
- L. Hsiao and Tao Luo, Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media, J. Differential Equations 125 (1996), no. 2, 329–365. MR 1378760, DOI https://doi.org/10.1006/jdeq.1996.0034
- 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 (1995), no. 3, 487–505. MR 1343463, DOI https://doi.org/10.1090/qam/1343463
- 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 (1995), no. 2, 480–503. MR 1362883, DOI https://doi.org/10.1006/jdeq.1995.1170
- Tai Ping Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc. 212 (1975), 375–382. MR 380135, DOI https://doi.org/10.1090/S0002-9947-1975-0380135-2
- Joel Smoller, Shock waves and reaction-diffusion equations, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York, 1994. MR 1301779
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
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)
C. J. Van Duyn and L. A. Peletier, A class of similarity solutions of the nonlinear diffusion equation, Nonlinear Analysis 1, 223–233 (1977)
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)
L. Hsiao and T. P. Liu, Nonlinear diffusive phenomena of nonlinear hyperbolic systems, Chinese Ann. Math. Ser. B 14, 465–480 (1993)
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)
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)
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)
Tai-ping Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc. 213, 375–382 (1975)
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1980
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
Article copyright:
© Copyright 1998
American Mathematical Society