Boundary effect on asymptotic behaviour of solutions to the p-system with linear damping

Journal of Differential Equations

Volumn 156, Issue 2, 1999, Pages 439-458

  Nishihara, Kenji ^a   Yang, Tong ^b  

^a WASEDA UNIVERSITY   (Japan)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033543057     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3598     Document Type: Article

References (16)

1. Duyn C. T., Van Peletier L. A. A class of similarity solutions of the nonlinear diffusion equation. Nonlinear Anal. TMA. 1:1997;223-233.
2. Hsiao L. Quasilinear Hyperbolic Systems and Dissipative Mechanisms. 1997;World Scientific, Singapore.
3. Hsiao L., Serre D. Global existence of solutions for the system of compressible adiabatic flow through porous media. SIAM J. Math. Anal. 27:1996;70-77.
4. Hsiao L., Liu T.-P. Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping. Commun. Math. Phys. 143:1992;599-605.
5. Hsiao L., Liu T.-P. Nonlinear diffusion phenomena of nonlinear hyperbolic system. Chinese Ann. Math. Ser. B. 14:1993;465-480.
6. Hsiao L., Luo T. Nonlinear diffusive phenomena of solutions for the system of compressible adiabatic flow through porous media. J. Differential Equations. 125:1996;329-365.
7. Liu T.-P., Matsumura A., Nishihara K. Behavior of solutions for the Burgers equations with boundary corresponding to rarefaction waves. SIAM J. Math. Anal. 29:1998;293-308.
8. Liu T.-P., Nishihara K. Asymptotic behavior for scalar viscous conservation laws with boundary effect. J. Differential Equations. 133:1997;296-320.
9. Liu T.-P., Yu S.-H. Propagation of stationary viscous Burgers shock under the effect of boundary. Arch. Rat. Mech. Anal. 139:1997;57-82.
10. P. Marcati, and, M. Mei, Convergence to nonlinear diffusion waves for solutions of the initial boundary problem to the hyperbolic conservation laws with damping, preprint.
11. Matsumura A. Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation. Publ. RIMS Kyoto Univ. 13:1977;349-379.
12. A. Matsumura, and, M. Mei, Asymptotics toward viscous shock profile for solution of the viscous p-system with boundary effect, Arch. Rat. Mech. Anal, to appear.
13. A. Matsumura, and, K. Nishihara, Global asymptotics towar the rarefaction wave for solutions of viscous p-system with boundary effect, Q. Appl. Math, to appear.
14. Nishihara K. Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping. J. Differential Equations. 131:1996;171-188.
15. Nishihara K. Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping. J. Differential Equations. 137:1997;384-395.
16. T. Pan, H. Liu, and, K. Nishihara, Asymptotic stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas with boundary, Jpn J. Ind. Appl. Math, to appear.