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
Full-text PDF Free Access
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Additional Information
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
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)
C. M. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana Univ. Math. J. 31, 471–491 (1982)
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)
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)
L. Hsiao and P. Marcati, Nonhomogeneous Quasilinear Hyperbolic Systems Arising in Chemical Engineering, Scuola Normale Superiore, Pisa, 1988, pp. 65–97
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.)
Tai-ping Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc. 213, 375–382 (1975)
Tai-ping Liu, Quasilinear hyperbolic systems, Comm. Math. Phys. 68, 141–172 (1979)
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)
Ta-tsien Li and Wen-ci Yu, Boundary value problems for quasilinear hyperbolic systems, Duke University Mathematics Series V, 1985
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
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1980
S. Q. Tang and L. Xiao, Global perturbation of the Riemann problem for the system of compressible flow through porous media (I)
S. Q. Tang and L. Xiao, Global perturbation of the Riemann problem for the system of compressible flow through porous media (II)
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)
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
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)
C. M. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana Univ. Math. J. 31, 471–491 (1982)
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)
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)
L. Hsiao and P. Marcati, Nonhomogeneous Quasilinear Hyperbolic Systems Arising in Chemical Engineering, Scuola Normale Superiore, Pisa, 1988, pp. 65–97
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.)
Tai-ping Liu, Existence and uniqueness theorems for Riemann problems, Trans. Amer. Math. Soc. 213, 375–382 (1975)
Tai-ping Liu, Quasilinear hyperbolic systems, Comm. Math. Phys. 68, 141–172 (1979)
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)
Ta-tsien Li and Wen-ci Yu, Boundary value problems for quasilinear hyperbolic systems, Duke University Mathematics Series V, 1985
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
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1980
S. Q. Tang and L. Xiao, Global perturbation of the Riemann problem for the system of compressible flow through porous media (I)
S. Q. Tang and L. Xiao, Global perturbation of the Riemann problem for the system of compressible flow through porous media (II)
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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Article copyright:
© Copyright 1995
American Mathematical Society
