Two dimensional exterior mixed problem for semilinear damped wave equations (Q705264)
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scientific article; zbMATH DE number 2131141
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two dimensional exterior mixed problem for semilinear damped wave equations |
scientific article; zbMATH DE number 2131141 |
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Two dimensional exterior mixed problem for semilinear damped wave equations (English)
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26 January 2005
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The author proves global existence, uniqueness and asymptotic decay of a solution to the two-dimensional exterior problem for the equation \(u_{tt}-\Delta u+u_{t}=| u| ^{p}\) \((t>0,x\in \Omega ,p>2),\) satisfying homogeneous Dirichlet boundary conditions and sufficiently small initial data with compact supports. He generalizes his previous results of the article [J. Differ. Equations 200, No. 1, 53--68 (2004; Zbl 1053.35105)] about radially symmetric solutions.
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asymptotic decay
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homogeneous Dirichlet boundary conditions
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small initial data
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global solution
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