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Existence and uniqueness of the global admissible solution for a viscoelastic model with relaxation

Published online by Cambridge University Press:  14 November 2011

Huijiang Zhao
Huijiang Zhao
Affiliation:
Young Scientist Laboratory of Mathematical Physics, Wuhan Institute of Mathematical Sciences, The Chinese Academy of Sciences, P.O. Box 71007, Wuhan 430071, P.R. China
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Abstract

This paper examines the Cauchy problem for a viscoelastic model with relaxation

with discontinuous, large initial data, where ½ ≦ μ <1, δ > 0 are constants. We first give a definition of admissible (or entropic) solutions to the system. Under this definition, we prove the existence, uniqueness and continuous dependence of the global admissible solution for the system. Our methods are essentially due to Kruzkov, and the requirement that f(u) is not badly degenerate (more precisely, meas {x: f″(x) = 0} = 0), needed previously when considering the global existence problem for the same system, is removed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 1113 - 1132
Copyright
Copyright © Royal Society of Edinburgh 1996

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