Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas

Communications in Mathematical Physics

Volumn 222, Issue 3, 2001, Pages 449-474

  Matsumura, Akitaka ^a   Nishihara, Kenji ^b  

^a OSAKA UNIVERSITY   (Japan)

^b WASEDA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035648890     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100517     Document Type: Article

References (13)

1. 1. Goodman, J.: Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Rat. Mech. Anal. 95, 325-344 (1986)
2. 2. Kawashima, S. and Nikkuni, Y.: Stability of stationary solutions to the half-space problem for the discrete Boltzmann equation with multiple collisions. Kyushu J. Math. to appear
3. 3. Kawashima, S. and Nishibata, S.: Stability of stationary waves for compressible Navier-Stokes equations in the half space. In preparation
4. 4. Liu, T.-P.: Nonlinear stability of shock waves for viscous conservation laws. Mem. Am. Math. Soc. 56, 1985
5. 5. Liu, T.-P., Matsumura, A. and Nishihara, K.: Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves. SIAM J. Math. Anal. 29, 293-308 (1998)
6. 6. Matsumura, A.: Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas. In: Proceedings of IMS Conference on Differential Equations from Mechnics, Hong Kong, 1999, to appear
7. 7. Matsumura, A. and Mei, M.: Convergence to traveling fronts of solutions of the p-system with viscosity in the presence of a boundary. Arch. Rat. Mech. Anal. 146, 1-22 (1999)
8. 8. Matsumura, A. and Nishihara, K.: On the stability of traveling wave solutions of a one-dimensional model system for compressible viscous gas. Japan J. Appl. Math. 2, 17-25 (1985)
9. 9. Matsumura, A. and Nishihara, K.: Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas. Jpn. J. Appl. Math. 3, 1-13 (1986)
10. 10. Matsumura, A. and Nishihara, K.: Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas. Commun. Math. Phys. 144, 325-335 (1992)
11. 11. Matsumura, A. and Nishihara, K.: Global asymptotics toward the rarefaction wave for solutions of viscous p-system with boundary effect. Q. Appl. Math. 58, 69-83 (2000)
12. 12. Szepessy, A. and Xin, Z.: Nonlinear stability of viscous shock waves. Arch. Rat. Mech. Anal. 122, 53-103 (1993)
13. 13. Xin, Z.: Asymptotic stability of rarefaction waves for 2 × 2 viscous hyperbolic conservation laws - two-mode case. J. Differ. Eqs. 78, 191-219 (1989)