Global solutions for nonlinear wave equations with localized dissipations in exterior domains
β Scribed by Makoto Nakamura
- Book ID
- 113699378
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 409 KB
- Volume
- 252
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
## 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
## Abstract We shall derive some global existence results to semilinear wave equations with a damping coefficient localized near infinity for very special initial data in __H__Γ__L__^2^. This problem is dealt with in the twoβdimensional exterior domain with a starβshaped complement. In our result,
Consider the initial boundary value problem for the linear dissipative wave equation ( + β t )u = 0 in an exterior domain β¦ β 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