The existence and stability of conic shock waves

Journal of Mathematical Analysis and Applications

Volumn 277, Issue 2, 2003, Pages 512-532

  Chen, Shuxing ^a   Geng, Zhenwen ^b   Li, Dening ^b  

^a FUDAN UNIVERSITY   (China)

^b WEST VIRGINIA UNIVERSITY   (United States)

Author keywords

Conic; Shock wave

Indexed keywords

EID: 0037439344     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00581-4     Document Type: Article

References (19)

1. S. Alinhac, Existence d'ondes de rarefaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equations 14 (1989) 173-230.
2. An Ton Bui, Dening Li, The double shock front solutions for hyperbolic conservation laws in multidimensional space, Trans. Amer. Math. Soc. 316 (1989) 233-250.
3. Shuxing Chen, Existence of local solution to supersonic flow past a three-dimensional wing, Adv. Appl. Math. 13 (1992) 273-304.
4. Shuxing Chen, Dening Li, Supersonic flow past a symmetrically curved cone, Indiana Univ. Math. J. 49 (2000) 1411-1435.
5. R. Courant, K.O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, New York, 1948.
6. L. Gårding, Le problème de la dérivée oblique pour l'équation des ondes, C. R. Acad. Sci. Paris Sér. A-B 285 (1977) 773-775.
7. O.A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, Springer, New York, 1985.
8. P.D. Lax, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math. 10 (1957) 537-566.
9. Dening Li, A one-phase hyperbolic Stefan problem in multi-dimensional space, Trans. Amer. Math. Soc. 318 (1990) 401-415.
10. Dening Li, Rarefaction and shock waves for multi-dimensional hyperbolic conservation laws, Comm. Partial Differential Equations 16 (1991) 425-450.
11. Tatsien Li, Wenci Yu, Boundary value problem for quasi-linear hyperbolic systems, Duke Univ. Math. Ser. 5 (1985).
12. A. Majda, One perspective on open problems in multi-dimensional conservation laws, IMA Vol. Math. Appl. 29 (1991) 217-238.
13. A. Majda, E. Thomann, Multi-dimensional shock fronts for second order wave equations, Comm. Partial Differential Equations 12 (1987) 777-828.
14. A.M. Meirmanov, On a classical solution of the multidimensional Stefan problem for quasilinear parabolic equations, Math. Sb. 112 (1980) 170-192.
15. G. Metivier, Interaction de deux chocs pour un système de deux lois de conservation en dimension deux d'espace, Trans. Amer. Math. Soc. 296 (1986) 431-479.
16. M. Mnif, Problème de Riemann pour une loi de conservation scalaire hyperbolique d'ordre deux, Comm. Partial Differential Equations 22 (1997) 1589-1627.
17. C.S. Morawetz, Potential theory for regular and Mach reflection of a shock at a wedge, Comm. Pure Appl. Math. 47 (1994) 593-624.
18. D.G. Schaeffer, Supersonic flow past a nearly straight wedge, Duke Math. J. 43 (1976) 637-670.
19. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, New York, 1983.