Stability of the E–H type regular shock refraction

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 Hölder space. The result obtained in this paper develops the theory of nonlinear mixed type equations and gives an application to a significant physical problem.