Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation
We consider the Cauchy problem for the n-dimensional generalized damped Boussinesq equation. Based on decay estimates of solutions to the corresponding linear equation, we define a solution space with time weighted norms. Under small condition on the initial value, the existence and asymptotic b...
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| Format: | Article |
| Language: | English |
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Texas State University
2012-06-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/96/abstr.html |
| Summary: | We consider the Cauchy problem for the n-dimensional generalized damped Boussinesq equation. Based on decay estimates of solutions to the corresponding linear equation, we define a solution space with time weighted norms. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in the corresponding Sobolev spaces are established by the contraction mapping principle. |
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| ISSN: | 1072-6691 |