Stability of strong detonation waves and rates of convergence

Electronic Journal of Differential Equations

Volumn 1998, Issue , 1998, Pages 1-17

  Li, Tong ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Asymptotic behavior; Shock wave; Strong detonation; Traveling wave; Weighted energy estimate

Indexed keywords

EID: 0002840914     PISSN: 10726691     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. R. Courant and K.O. Friedrichs, Supersonic flow and shock waves, Springer Verlag, 1948.
2. J.J. Erpenbeck, Stability of steady-state equilibrium detonations, Phys. Fluids, 5(1961) 604-614.
3. W. Fickett, Decay of small planar perturbations on a strong steady detonation: A differential-difference equation for shock, Phys. Fluids, 30(1987)1299-1309.
4. W. Fickett and W.C. Davis, Detonation, University of California Press,1979.
5. J. Goodman, Nonlinear asymptotic stability of viscous shock prole for conservation laws, Arch. Rat. Mech. Anal., 95(1986) 325-344.
6. S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solution to system for one dimensional gas motion, Comm. Math. Phys.,101(1985) 97-127.
7. P.D. Lax, Hyperbolic systems of conservation laws, II., Comm. Pure Appl. Math., 10(1957) 537-566.
8. T. Li, On the initiation problem for a combustion model, J. Diff. Eqns.,112(1994) 351-373.
9. T. Li, On the Riemann problem for a combustion model, SIAM J. Math. Anal., 24(1993), 59-75.
10. T. Li, Rigorous asymptotic stability of a CJ detonation wave in the limit of small resolved heat release, Combustion Theory and Modeling, 1(1997)259-270.
11. T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Mem. Amer. Math. Soc. 328, (1985).
12. T.-P. Liu and Z. Xin, Stability of viscous shock waves associated with a system of nonstrictly hyperbolic conservation laws, Comm. Pure Appl. Math., 45(1992) 361-388.
13. T.-P. Liu and L. A. Ying, Nonlinear stability of strong detonations for a viscous combustion model, SIAM J. Math. Anal., 26(1995) 519-528.
14. R. Rosales and A. Majda, Weakly nonlinear detonation waves, SIAM J. Appl. Math, 43(1983) 1086-1118.