Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws

Memoirs of the American Mathematical Society

Volumn 125, Issue 599, 1997, Pages

  Liu, Tai Ping ^a   Zeng, Yanni ^a  

^a NONE

Author keywords

Compressible Navier Stokes equations; Conservation laws; Green's function; Large time behavior; Magnetohydrodynamics; Nonlinear and linear diffusion waves; Quasilinear hyperbolic parabolic systems

Indexed keywords

EID: 5844381969     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: 10.1090/memo/0599     Document Type: Article

References (21)

1. M. Brio and C. C. Wu, An upwind differencing scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys. 75 (1988), 400-422.
2. J. B. Butler, Jr., Perturbation series for eigenvalues of analytic non-symmetric operators, Arch. Math. 10 (1959), 21-27.
3. I-L. Chern, Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws, Comm. Math. Phys. 138 (1991), 51-61.
4. J. D. Cole, On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9 (1951), 225-236.
5. H. Freistühler, Rotational degeneracy of hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 113 (1991), 39-64.
6. K. O. Friedrichs and P. D. Lax, Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 1686-1688.
7. D. Hoff, Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data, Proc. Roy. Soc. Edinburgh 103A (1986), 301-315.
8. xx, Comm. Pure Appl. Math. 3 (1950), 201-230.
9. T. Kato, Perturbation theory for linear operators, 2nd edn., Springer, New York, 1976.
10. S. Kawashima, Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Doctoral thesis, Kyoto University, 1983.
11. S. Kawashima, Large-time behavior of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. Roy. Soc. Edinburgh 106A (1987), 169-194.
12. S. Kawashima and M. Okada, Smooth global solutions for the one-dimensional equations in magnetohydrodynamics, Proc. Japan Acad. Ser. A 58 (1982), 384-387.
13. L. D. Landau, E. M. Lifshitz and L. P. Pitaevskiǐ, Electrodynamics of continuous media, 2nd edn., Pergamon Press, New York, 1984.
14. P. D. Lax, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math. 10 (1957), 537-566.
15. T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. Am. Math. Soc. 56 (1985), no. 328.
16. T.-P. Liu, Interactions of nonlinear hyperbolic waves, Nonlinear Analysis (F.-C. Liu and T.-P. Liu, eds.), World Scientific, Singapore, 1991, pp. 171-184.
17. Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985), 249-275.
18. J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, 1983.
19. T. Umeda, S. Kawashima and Y. Shizuta, On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984), 435-457.
20. 1 asymptotic behavior of compressible, isentropic, viscous 1-D flow, Comm. Pure Appl. Math. 47 (1994), 1053-1082.
21. p asymptotic behavior of solutions to hyperbolic-parabolic systems of conservation laws, Arch. Math, (to appear).