Global Stability of E-H Type Regular Refraction of Shocks on the Interface between Two Media
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Wed, 18/04/2012 12:30 |
Beixiang Fang (Shanghai JiaoTong University - OxPDE visitor) |
OxPDE Lunchtime Seminar  |
Gibson 1st Floor SR |
| In this talk I will discuss the refraction of shocks on the interface for 2-d steady compressible flow. Particularly, the class of E-H type regular refraction is defined and its global stability of the wave structure is verified. The 2-d steady potential flow equations is employed to describe the motion of the fluid. The stability problem of the E-H type regular refraction can be reduced to a free boundary problem of nonlinear mixed type equations in an unbounded domain. The corresponding linearized problem has similarities to a generalized Tricomi problem of the linear 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 the corresponding nonlocal operator in a weighted Hölder space via careful harmonic analysis. This is a joint work with CHEN Shuxing and HU Dian. | |||