Asymptotic behavior of solutions to wave equations with a memory condition at the boundary (Q2761580)
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scientific article; zbMATH DE number 1685994
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic behavior of solutions to wave equations with a memory condition at the boundary |
scientific article; zbMATH DE number 1685994 |
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24 January 2002
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integral boundary condition
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polynomial decay
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0.9563305
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0.9436841
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0.93806416
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0.91972756
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0.9162539
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Asymptotic behavior of solutions to wave equations with a memory condition at the boundary (English)
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The author studies asymptotic behavior of the solutions to the wave equation \(u_{tt}-a(t)u_{xx}=0\), \(x\in (0,1)\), \(t>0, \) with boundary conditions including an integral operator representing memory effect. He proves polynomial decay of the solution (for \(t\rightarrow \infty\)), if the kernel of the integral operator decays polynomially and exponential decay, if the kernel decays exponentially.
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