Dissipative structure and entropy for hyperbolic systems of balance laws

Archive for Rational Mechanics and Analysis

Volumn 174, Issue 3, 2004, Pages 345-364

  Kawashima, S ^a   Yong, W A ^b  

^a KYUSHU UNIVERSITY   (Japan)

^b UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12444288058     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-004-0330-9     Document Type: Article

References (12)

1. CHEN, G.-Q., LEVERMORE, C.D., LIU, T.-P.: Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. 47, 787-830 (1994)
2. FRIEDRICHS, K.O., LAX, P.D.: Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. USA 68, 1686-1688 (1971)
3. GODUNOV, S.K.: An interesting class of quasilinear systems. Dokl. Akad. Nauk SSSR 139, 521-523 (1961)
4. HANOUZET, B., NATALINI, R.: Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy. Arch. Rational Mech. Anal. 169, 89-117 (2003)
5. KAWASHIMA, S.: Global existence and stability of solutions for discrete velocity models of the Boltzmann equation. Recent Topics in Nonlinear PDE, Lecture Notes in Num. Appl. Anal. 6, Kinokuniya, Tokyo, 1983, 59-85
6. KAWASHIMA, S.: Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics. Doctoral Thesis, Kyoto University, 1984
7. KAWASHIMA, S.: Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications. Proc. Roy. Soc. Edinburgh Sect. A 106, 169-194 (1987)
8. KAWASHIMA, S., SHIZUTA, Y.: On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws. Tôhoku Math. J. 40, 449-464 (1988)
9. KAWASHIMA, S., SHIZUTA Y.: The Navier-Stokes equation in the discrete kinetic theory. J. Méc. Théor.Appl. 7, 597-621 (1988)
10. SHIZUTA, Y., KAWASHIMA, S.: Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation. Hokkaido Math. J. 14, 249-275 (1985)
11. YONG, W.-A.: Basic aspects of hyperbolic relaxation systems. In Advances in the Theory of Shock Waves, FREISTÜHLER, H., SZEPESSY, A. eds., Birkhäuser Series Progress in Nonlinear Differential Equations and Their Applications, Vol. 47, Birkhäuser, Boston, 2001, 259-305
12. YONG, W.-A.: Entropy and global existence for hyperbolic balance laws. Arch. Rational Mech. Anal. 172, 247-266 (2004)