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 |
| Summary: | 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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| ISSN: | 1110-757X 1687-0042 |