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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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/2708483 |
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| _version_ | 1832550874008780800 |
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| author | Hongjun Qiu Yinghui Zhang |
| author_facet | Hongjun Qiu Yinghui Zhang |
| author_sort | Hongjun Qiu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-e97d0c61929f44bcaf7715bc558675c4 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-e97d0c61929f44bcaf7715bc558675c42025-02-03T06:05:37ZengWileyAdvances 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 |
| spellingShingle | Hongjun Qiu Yinghui Zhang Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping Advances in Mathematical Physics |
| title | 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_short | Decay of the 3D Quasilinear Hyperbolic Equations with Nonlinear Damping |
| title_sort | decay of the 3d quasilinear hyperbolic equations with nonlinear damping |
| url | http://dx.doi.org/10.1155/2017/2708483 |
| work_keys_str_mv | AT hongjunqiu decayofthe3dquasilinearhyperbolicequationswithnonlineardamping AT yinghuizhang decayofthe3dquasilinearhyperbolicequationswithnonlineardamping |