References
- Bressan , A and Jenssen , HK . 2000 . On the convergence of Godunov cheme for nonlinear hyperbolic systems . Chin. Ann. Math. , 21B ( 3 ) : 269 – 284 .
- Hamer , K . 1971 . Nonlinear effects on the propagation of sound waves in a radiating gas . Quart. J. Mech. Appl. Math. , 24 : 155 – 168 .
- Iguchi , T and Kawashima , S . 2002 . On space-time decay properties of solutions to hyperbolic-elliptic coupled systems . Hiroshima Math. J , 32 ( 2 ) : 229 – 308 .
- Kawashima S Nikkuni Y Nishibata S 1999 The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics Analysis of Systems of Conservation Laws (Aachen, 1997), pp. 87–127, Chapman and Hall/CRC Monogr. Surv. Pure Appl. Math., 99 Chapman and Hall/CRC Boca Raton FL
- Kawashima , S and Nishibata , S . 1999 . Cauchy problem for a model system of the radiating gas: weak solutions with a jump and classical solutions . Math. Models Methods Appl. Sci. , 9 ( 1 ) : 69 – 91 .
- Kawashima , S and Nishibata , S . 1999 . Shock waves for a model system of the radiating gas . SIAM J. Math. Anal. , 30 ( 1 ) : 95 – 117 .
- Kawashima , S and Nishibata , S . 2001 . A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics . Indiana Univ. Math. J. , 50 ( 1 ) : 567 – 589 .
- Lax , PD . 1957 . Hyperbolic systems of conservation laws II . Comm. Pure Appl. Math. , 10 : 537 – 566 .
- Lin , L-W and Yang , T . 1991 . Convergence of the Lax-Friedrichs' scheme for isentropic gas dynamics in Lagrangian coordinates . Commun. Partial Differential Equations , 16 ( 8 and 9 ) : 1441–1460.
- Lattanzio , C and Marcati , P . 2003 . Global well-posedness and relaxation limits of a model for radiating gas . Journal of Differential Equations , 190 : 439 – 465 .
- Nishibata , S . 2000 . Asymptotic behavior of solutions to a model system of radiating gas with discontinuous initial data . Math. Models Methods Appl. Sci. , 10 ( 8 ) : 1209 – 1231 .
- Oleinik , OA . 1963 . Discontinuous solutions of nonlinear differential equations . Amer. Math. Soc. Transl. Ser.2 , 26 ( 1963 ) : 95–172.
- Serre D Stabilite L 1 des chocs et de deux types de profils, pour des lois de conservation scalaries (preprint)
- Yang , T , Zhao , H-J and Zhu , C-J . 2003 . BV estimates of Lax-Friedrichs's scheme for a class of nonlinear hyperbolic conservation laws . Proceedings of the American Mathematical Society , 131 ( 4 ) : 1257 – 1266 .
- Vincenti WG Kruger CH 1965 Introduction to Physical Gas Dynamics, Wiley New York