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.
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
.
DOI: 10.1007/s10473-021-0407-7
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