SHOCK DIFFRACTION PROBLEM BY CONVEX CORNERED WEDGES FOR ISOTHERMAL GAS

doi:10.1007/s10473-021-0407-7

Abstract

Abstract: We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave system. We reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded domain. The degeneracy is of Keldysh type-the derivative of a solution blows up at the boundary. We establish the global existence of solutions and prove the $C^{0,\frac{1}{2}}$-regularity of solutions near the degenerate boundary. We also compare the difference of solutions between the isothermal gas and the polytropic gas.

Key words: Nonlinear wave system, isothermal gas, shock diffraction, degenerate elliptic equation, Riemann problem, regularity

CLC Number:

35M10

Qin WANG, Kyungwoo SONG. SHOCK DIFFRACTION PROBLEM BY CONVEX CORNERED WEDGES FOR ISOTHERMAL GAS[J].Acta mathematica scientia,Series B, 2021, 41(4): 1130-1140.

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