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 \({C^{0,{1 \over 2}}}\)-regularity of solutions near the degenerate boundary. We also compare the difference of solutions between the isothermal gas and the polytropic gas.

中文翻译：

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等温气体的凸角楔冲击衍射问题

我们关注由非线性波系统守恒定律建模的等温气体的激波衍射构型。我们将激波衍射问题重新表述为固定有界域中的线性退化椭圆方程。简并是 Keldysh 类型的——解的导数在边界处爆炸。我们建立了解的全局存在性并证明了在退化边界附近解的\({C^{0,{1 \over 2}}}\) -正则性。我们还比较了等温气体和多方气体之间的溶液差异。