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Global solution to a three-dimensional spherical piston problem for the relativistic Euler equations

Part of: Hyperbolic equations and systems

Published online by Cambridge University Press:  23 September 2020

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GENG LAI*
Affiliation:
Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China email: laigeng@shu.edu.cn
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Abstract

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we consider a ‘spherical piston’ problem for the relativistic Euler equations, which describes the wave motion produced by a sphere expanding into an infinite surrounding medium. We use the reflected characteristics method to construct a global piecewise smooth solution with a single shock of this spherical piston problem, provided that the speed of the sphere is a small perturbation of a constant speed.

Keywords

Relativistic Euler equationsspherical piston problemshock wavecharacteristic

MSC classification

Primary: 35L65: Conservation laws
Secondary: 35L60: Nonlinear first-order hyperbolic equations 35L67: Shocks and singularities
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 1 , February 2022 , pp. 1 - 26
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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