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Resolution of the spherical piston problem for compressible isentropic gas dynamics via a self-similar viscous limit

Published online by Cambridge University Press:  14 November 2011

M. Slemrod
M. Slemrod
Affiliation:
Center for the Mathematical Sciences, University of Wisconsin-Madison, Madison, WI 53715-1149, U.S.A.
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Abstract

This paper proves the existence of solutions to the spherical piston problem for isentropic gas dynamics with equation of state p(p) = Apγ, γ≧ 1. The method of analysis is to replace the usual viscosity ε with εt, thus permitting a search for self-similar viscous limits. The main result of the paper is that self-similar viscous limits are proved to exist and converge to a solution to the piston problem when

N = 1, 2, 3 space dimensions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1309 - 1340
Copyright
Copyright © Royal Society of Edinburgh 1996

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