## Abstract Let __u__ and __v__ be, respectively, the solutions to the Cauchy problems for the dissipative wave equation $$u\_{tt}+u\_tβ\Delta u=0$$\nopagenumbers\end and the heat equation $$v\_tβ\Delta v=0$$\nopagenumbers\end We show that, as $t\rightarrow+\infty$\nopagenumbers\end, the norms
On L1 decay problem for the dissipative wave equation
β Scribed by Kosuke Ono
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 117 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.391
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β¦ Synopsis
Abstract
We study the decay estimates of solutions to the Cauchy problem for the dissipative wave equation in one, two, and three dimensions. The representation formulas of the solutions provide the sharp decay rates on L^1^ norms and also L^p^ norms. Copyright Β© 2003 John Wiley & Sons, Ltd.
π SIMILAR VOLUMES
We study the asymptotic behavior of solutions of dissipative wave equations with space-time-dependent potential. When the potential is only time-dependent, Fourier analysis is a useful tool to derive sharp decay estimates for solutions. When the potential is only space-dependent, a powerful techniqu
## Abstract We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain Ξ© with the boundary βΞ© = Ξ~0~ βͺ Ξ~1~, Ξ~0~ β© Ξ~1~ = β οΈ. We impose the homogeneous Dirichlet condition on Ξ~0~ and a dissipative Neumann condition on