Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation
We consider the Cauchy problem for the damped nonlinear hyperbolic equation in n-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/353757 |
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doaj-da741762a13640fe88577ad3177233e52020-11-24T23:25:27ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/353757353757Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic EquationYu-Zhu Wang0School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaWe consider the Cauchy problem for the damped nonlinear hyperbolic equation in n-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle.http://dx.doi.org/10.1155/2013/353757 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yu-Zhu Wang |
| spellingShingle |
Yu-Zhu Wang Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation Journal of Applied Mathematics |
| author_facet |
Yu-Zhu Wang |
| author_sort |
Yu-Zhu Wang |
| title |
Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation |
| title_short |
Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation |
| title_full |
Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation |
| title_fullStr |
Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation |
| title_full_unstemmed |
Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation |
| title_sort |
asymptotic behavior of solutions to the damped nonlinear hyperbolic equation |
| publisher |
Hindawi Limited |
| series |
Journal of Applied Mathematics |
| issn |
1110-757X 1687-0042 |
| publishDate |
2013-01-01 |
| description |
We consider the Cauchy problem for the damped nonlinear hyperbolic equation in n-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle. |
| url |
http://dx.doi.org/10.1155/2013/353757 |
| work_keys_str_mv |
AT yuzhuwang asymptoticbehaviorofsolutionstothedampednonlinearhyperbolicequation |
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