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Existence of a global smooth solution to the initial boundary-value problem for the p-system with nonlinear damping

Published online by Cambridge University Press:  03 December 2013

Mina Jiang ,
Dong Li  and
Lizhi Ruan
Mina Jiang
Affiliation:
Laboratory of Nonlinear Analysis, Department of Mathematics, Huazhong Normal University, Wuhan 430079, People's Republic of China (jmn3911@gmail.com)
Dong Li
Affiliation:
Laboratory of Nonlinear Analysis, Department of Mathematics, Huazhong Normal University, Wuhan 430079, People's Republic of China (jmn3911@gmail.com)
Lizhi Ruan
Affiliation:
Laboratory of Nonlinear Analysis, Department of Mathematics, Huazhong Normal University, Wuhan 430079, People's Republic of China (jmn3911@gmail.com)
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Abstract

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This paper is concerned with the initial boundary-value problem for the p-system with nonlinear damping. We prove the existence of a global smooth solution under the assumption that only the C0-norm of the derivative of the initial data is sufficiently small, while the C0-norm of the initial data is not necessarily small. The proof is based on several key a priori estimates, the maximum principle and the characteristic method.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 6 , December 2013 , pp. 1243 - 1253
Copyright
Copyright © Royal Society of Edinburgh 2013