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

Memoirs of the American Mathematical Society

Volumn , Issue 599, 1997, Pages 1-120

  Liu, Tai Ping ^a   Zeng, Yanni ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030642440     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. [BW] M. Brio and C. C. Wu, An upwind differencing scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys. 75 (1988), 400-422.
2. [Bu] J. B. Butler, Jr., Perturbation series for eigenvalues of analytic non-symmetric operators, Arch. Math. 10 (1959), 21-27.
3. [Ch] I-L. Chern, Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws, Comm. Math. Phys. 138 (1991), 51-61.
4. [Co] J. D. Cole, On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9 (1951), 225-236.
5. [Fr] H. Freistühler, Rotational degeneracy of hyperbolic systems of conservation laws, Arch. Rational Mech. Anal. 113 (1991), 39-64.
6. [FL] 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. [H] 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. [Kt] T. Kato, Perturbation theory for linear operators, 2nd edn., Springer, New York, 1976.
10. [K] S. Kawashima, Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Doctoral thesis, Kyoto University, 1983.
11. [Ka] 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. [KO] 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. [LLP] L. D. Landau, E. M. Lifshitz and L. P. Pitaevskiǐ, Electrodynamics of continuous media, 2nd edn., Pergamon Press, New York, 1984.
14. [La] P. D. Lax, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math. 10 (1957), 537-566.
15. [L] T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. Am. Math. Soc. 56 (1985), no. 328.
16. [Liu] 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. [SK] 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. [Sm] J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, New York, 1983.
19. [UKS] 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).