Stability of the E-H type regular shock refraction

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• 作者：Shuxing Chen^a ; ^{sxchen@fudan.edu.cn} ; Dian Hu^a ; ^{dean.huu@gmail.com} ; Beixiang Fang^b ; ^{bxfang@sjtu.edu.cn}
• 关键词：35L65 ; 35L67 ; 35M10 ; 35B35 ; 76N10
• 刊名：Journal of Differential Equations
• 出版年：2013
• 出版时间：15 April, 2013
• 年：2013
• 卷：254
• 期：8
• 页码：3146-3199
• 全文大小：659 K

文摘

In this paper the refraction of shocks on the interface for 2-D steady compressible flow is discussed. Particularly, the E-H type regular refraction is defined and its global stability of the wave structure is proved. The 2-D steady potential flow equation is employed to describe the motion of the fluid. The stability of the E-H type regular refraction can be reduced to a free boundary problem of a nonlinear mixed type equation in an unbounded domain. The corresponding linearized problem is a generalized Tricomi problem of the Lavrentiev-Bitsadze mixed type equation, and it can be reduced to a nonlocal boundary value problem of an elliptic system. The later is finally solved by establishing the bijection of a corresponding nonlocal operator in a weighted H?lder space. The result obtained in this paper develops the theory of nonlinear mixed type equations and gives an application to a significant physical problem.