Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping

Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping

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...

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Main Authors: Hongjun Qiu, Yinghui Zhang
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2017/2708483
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spelling doaj-e97d0c61929f44bcaf7715bc558675c42021-07-02T07:57:32ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/27084832708483Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear DampingHongjun Qiu0Yinghui Zhang1College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, ChinaDepartment of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, ChinaWe 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 H3-norm. Furthermore, if, additionally, Lp-norm (1≤p<6/5) of the initial perturbation is finite, we also prove the optimal Lp-L2 decay rates for such a solution without the additional technical assumptions for the nonlinear damping f(v) given by Li and Saxton.http://dx.doi.org/10.1155/2017/2708483
collection DOAJ
language English
format Article
sources DOAJ
author Hongjun Qiu
Yinghui Zhang
spellingShingle Hongjun Qiu
Yinghui Zhang
Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping
Advances in Mathematical Physics
author_facet Hongjun Qiu
Yinghui Zhang
author_sort Hongjun Qiu
title Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping
title_short Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping
title_full Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping
title_fullStr Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping
title_full_unstemmed Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping
title_sort decay of the 3d quasilinear hyperbolic equations with nonlinear damping
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2017-01-01
description 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 H3-norm. Furthermore, if, additionally, Lp-norm (1≤p<6/5) of the initial perturbation is finite, we also prove the optimal Lp-L2 decay rates for such a solution without the additional technical assumptions for the nonlinear damping f(v) given by Li and Saxton.
url http://dx.doi.org/10.1155/2017/2708483
work_keys_str_mv AT hongjunqiu decayofthe3dquasilinearhyperbolicequationswithnonlineardamping
AT yinghuizhang decayofthe3dquasilinearhyperbolicequationswithnonlineardamping
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