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Self-similar solutions of the spherically symmetric Euler equations for general equations of state. (English) Zbl 1479.35186

Summary: The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we construct rigorously self-similar solutions to the Riemann problem of the spherically symmetric Euler equations for general equations of state. We use the assumption of self-similarity to reduce the spherically symmetric Euler equations to a system of nonlinear ordinary differential equations, from which we obtain detailed structures of solutions besides their existence.

MSC:

35C06 Self-similar solutions to PDEs
35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35Q31 Euler equations
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