Cauchy problem for a model system of the radiating gas: Weak solutions with a jump and classical solutions

Mathematical Models and Methods in Applied Sciences

Volumn 9, Issue 1, 1999, Pages 69-91

  Kawashima, Shuichi ^a   Nishibata, Shinya ^b  

^a KYUSHU UNIVERSITY   (Japan)

^b FUKUOKA INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033483284     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202599000063     Document Type: Article

References (11)

1. A. T. Cates and D. G. Crighton, Nonlinear diffraction and caustic formation, Proc. R. Soc. London A430 (1990) 69-88.
2. D. G. Crighton, Model equations of nonlinear acoustics, Ann. Rev. Fluid Mech. 11 (1979) 11-33.
3. K. Hamer, Nonlinear effects on the propagation of sounds waves in a radiating gas, Quarter J. Mech. Appl. Math. 24 (1971) 155-168.
4. t + (σ - μf(u)) = 0, Arch. Rational Mech. Anal. 82 (1983) 87-108.
5. D. Hoff and T.-P. Liu, The inviscid limit for the Navier-Stokes equations of compressible isentropic flow with shock data, Indiana Univ. Math. J. 38 (1989) 861-915.
6. K. Ito, BV-solutions of the hyperbolic-elliptic system for a radiating gas, to appear.
7. S. Kawashima, Large-time behavior of solutions to hyperbolic-parabolic system of conservation laws and applications, Proc. R. Soc. Edinburgh A106 (1987) 169-194.
8. S. Kawashima and S. Nishibata, Shock waves for a model system of the radiating gas, to appear in SIAM J. Math. Anal.
9. S. Kawashima and Y. Tanaka, Asymptotic behavior of solutions to the one-dimensional model system for Radiating gas, to appear.
10. S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR Sbor. 10 (1970) 217-243.
11. W. G. Vincenti and C. H. Kruger, Introduction to Physical Gas Dynamics (Wiley, 1965).