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Decay estimates for dissipative wave equations in exterior domains

โœ Scribed by Kosuke Ono

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
273 KB
Volume
286
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

Consider the initial boundary value problem for the linear dissipative wave equation ( + โˆ‚ t )u = 0 in an exterior domain โ„ฆ โŠ‚ R N . Using the so-called cut-off method together with local energy decay and L 2 decays in the whole space, we study decay estimates of the solutions. In particular, when N 3, we derive L p decays with p 1 of the solutions. Next, as an application of the decay estimates for the linear equation, we consider the global solvability problem for the semilinear dissipative wave equations ( + โˆ‚ t )u = f (u) with f (u) = |u| ฮฑ+1 , |u| ฮฑ u in an exterior domain.

๐Ÿ“œ SIMILAR VOLUMES

L1 Decay estimates for dissipative wave
L1 Decay estimates for dissipative wave equations
โœ Albert Milani; Yang Han ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 151 KB

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

Energy decay for the wave equation with
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โœ Jeong Ja Bae; Mitsuhiro Nakao ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 186 KB

## Abstract We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain ฮฉ with the boundary โˆ‚ฮฉ = ฮ“~0~ โˆช ฮ“~1~, ฮ“~0~ โˆฉ ฮ“~1~ = โˆ…๏ธ. We impose the homogeneous Dirichlet condition on ฮ“~0~ and a dissipative Neumann condition on