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Energy decay and partition for dissipative wave equations

✍ Scribed by Jerome A Goldstein; Steven I Rosencrans


Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
299 KB
Volume
36
Category
Article
ISSN
0022-0396

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πŸ“œ SIMILAR VOLUMES


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## Abstract Let __u__ and __v__ be, respectively, the solutions to the Cauchy problems for the dissipative wave equation $$u\_{tt}+u\_t‐\Delta u=0$$\nopagenumbers\end and the heat equation $$v\_t‐\Delta v=0$$\nopagenumbers\end We show that, as $t\rightarrow+\infty$\nopagenumbers\end, the norms

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## 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 βˆ‚Ξ© = Ξ“~0~ βˆͺ Ξ“~1~, Ξ“~0~ ∩ Ξ“~1~ = βˆ…οΈ. We impose the homogeneous Dirichlet condition on Ξ“~0~ and a dissipative Neumann condition on

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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

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We derive a fast decay estimate for the wave equation with a local degenerate dissipation of the type a(x)u t in a bounded domain Ω. The dissipative coefficient a(x) is a nonnegative function only on a neighborhood of some part of the boundary βˆ‚β„¦ and may vanish somewhere in Ω. The results obtained e

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✍ Kosuke Ono πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 117 KB

## 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.