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Advances in Mathematical Physics
Volume 2017, Article ID 2708483, 13 pages
https://doi.org/10.1155/2017/2708483
Research Article

Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping

1College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
2Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China

Correspondence should be addressed to Yinghui Zhang; moc.621@0190iuhgniygnahz

Received 13 February 2017; Accepted 19 April 2017; Published 23 May 2017

Academic Editor: Ming Mei

Copyright © 2017 Hongjun Qiu and Yinghui Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the 3D quasilinear hyperbolic equations with nonlinear damping which describes the propagation of heat wave for rigid solids at very low temperature, below about 20 K. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in the sense of -norm. Furthermore, if, additionally, -norm () of the initial perturbation is finite, we also prove the optimal decay rates for such a solution without the additional technical assumptions for the nonlinear damping given by Li and Saxton.