Nonlinear stability of weak detonation waves for a combustion model

Communications in Mathematical Physics

Volumn 204, Issue 3, 1999, Pages 551-586

  Liu, Tai Ping ^a   Yu, Shih Hsien ^b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033245368     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050657     Document Type: Article

References (17)

1. 1. Courant, R. & Friedrichs, K.O.: Supersonic Flow and Shock Waves. Berlin-Heidelberg-New York: Springer-Verlag, 1948
2. 2. Gasser, I., Szmolyan, P.: A geometric singular perturbation analysis of detonation and deflagration waves, SIAM J. Math. Anal. 24, 968-986 (1993)
3. 3. Gustafsson, B., Kreiss, H.-O., Oliger, J.: Time Dependent Problems and Difference Methods. New York: Wiley-Interscience, 1995
4. 4. Kreiss, G. & Kreiss, H.-O.: Stability of systems of viscous conservation laws. Comm. Pure and Appl. Math.51, 1397-1424 (1998)
5. 5. Li, T.: Stability of strong detonation waves and rates of convergence. Electronic J. of Differential Equations 1-17 (1998)
6. 6. Li, T.: Rigorous asymptotic staility of a Chapman-Jouguet detonation wave in the limit of small resolved heat release. Combustion Theory Modeling 1, 259-270 (1997)
7. 7. Liu, T.-P.: Pointwise Convergence to Shock Waves for Viscous Conservation Laws. Comm. Pure and Appl. Math. vol. L No 11, 1113-1182 (1997)
8. 8. Liu, T.-P.: Zero dissipation and stability of shocks. Method and Applications of Analysis 5, 81-94 (1998)
9. 9. Liu, T.-P. & Ying, L.-A.: Nonlinear stability of strong detonation for a viscous combustion model. SIAM J. Math. Anal. 26, 519-528 (1995)
10. 10. Liu, T.-P. & Yu, S.-H.: Propagation of a Stationary Shock Layer in the Presence of a Boundary. Arch. Rat. Mech. Anal. 139, 57-82 (1997)
11. 11. Liu, T.-P. & Yu, S.-H.: Continuum Shock Profiles for Discrete Conservation Laws, I. Construction. To appear in Commun. Pure Appl. Math. (1999)
12. 12. Liu, T.-P. & Yu, S.-H.: Continuum Shock Profiles for Discrete Conservation Laws, II: Stability. Submitted to Commun. Pure Appl. Math. (1998)
13. 13. Majda, A.: A qualitative model for dynamics combustion. SIAM J. Appl. Math. 37, 686-699 (1979)
14. 14. Nishibata, S. & Yu, S.-H.: The Asymptotic Behavior of the Hyperbolic Conservation Laws with Relaxation on the Quarter Plane. SIAM J. Appl. Math. 28, 304-321 (1997)
15. 15. Rosales, R. & Majda, A.: Weakly nonlinear detonation waves. SIAM J. Appl. Math. 43, 1086-1118 (1983)
16. 16. Szepessy, A.: Dynamics and Stability of a weak detonation wave. Preprint
17. 17. Yu, S.-H.: Zero Dissipation Limit to Solutions with Shocks for Systems of Hyperbolic Conservation Laws. To appear in Arch. Rat. Mech. Anal.