Time-asymptotic behavior of wave propagation around a viscous shock profile

Communications in Mathematical Physics

Volumn 290, Issue 1, 2009, Pages 23-82

  Liu, Tai Ping ^a,b   Zeng, Yanni ^c  

^a INSTITUTE OF MATHEMATICS   (Taiwan)

^b STANFORD UNIVERSITY   (United States)

^c UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349673846     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-009-0820-6     Document Type: Article

References (20)

1. Chern I.-L.: Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws. Commun. Math. Phys. 138, 51-61 (1991).
2. Cole J.D.: On a quasi-linear parabolic equation occurring in aerodynamics. Quart. Appl. Math. 9, 225-236 (1951).
3. Goodman J.: Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Rat. Mech. Anal. 95, 325-344 (1986).
4. xx. Comm. Pure Appl. Math. 3, 201-230 (1950).
5. Lax P.D.: Hyperbolic systems of conservation laws, II. Comm. Pure Appl. Math. 10, 537-566 (1957).
6. Liu, T.-P.: Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc. 56(328), v+108 pp. (1985).
7. Liu, T.-P.: Interactions of nonlinear hyperbolic waves. In: Nonlinear Analysis, Liu, F.-C., Liu, T.-P. (eds)., Singapore: World Scientific, 1991, pp. 171-184.
8. Liu T.-P.: Pointwise convergence to shock waves for viscous conservation laws. Comm. Pure Appl. Math. 50, 1113-1182 (1997).
9. Liu, T.-P., Zeng, Y.: Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws. Mem. Amer. Math. Soc. 125(599), viii+120 pp. (1997).
10. Liu T.-P., Zeng Y.: Compressible Navier-Stokes equations with zero heat conductivity. J. Diff. Eqs. 153, 225-291 (1999).
11. Liu, T.-P., Zeng, Y.: Fundamental solution for hyperbolic-parabolic system around a shock profile. Preprint.
12. Matsumura A., Nishihara K.: On a stability of travelling wave solution of a one-dimensional model system for compressible viscous gas. Japan J. Appl. Math. 3, 1-13 (1986).
13. Shu C.-W., Zeng Y.: High-order essentially non-oscillatory scheme for viscoelasticity with fading memory. Quart. Appl. Math. 55, 459-484 (1997).
14. Smoller J.: Shock Waves and Reaction-Diffusion Equations 2nd ed. Springer-Verlag, New York (1994).
15. Szepessy A., Xin Z.P.: Nonlinear stability of viscous shock waves. Arch. Rat. Mech. Anal. 122, 53-103 (1993).
16. 1 asymptotic behavior of compressible, isentropic, viscous 1-D flow. Comm. Pure Appl. Math. 47, 1053-1082 (1994).
17. p asymptotic behavior of solutions to hyperbolic-parabolic systems of conservation laws. Arch. Math. (Basel) 66, 310-319 (1996).
18. Zeng Y.: Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation. Arch. Rat. Mech. Anal. 150, 225-279 (1999).
19. Zeng, Y.: Gas Flows with Several Thermal Nonequilibrium Modes. Arch. Rat. Mech. Anal. (to appear).
20. Zumbrum, K.: Planar stability criteria for viscous shock waves of systems with real viscosity. In: Hyperbolic Systems of Balance Laws, Lecture Notes in Math. 1911, Berlin: Springer, 2007, pp. 229-326.