Solutions of the wave equation with localized energy
β Scribed by James V. Ralston
- Publisher
- John Wiley and Sons
- Year
- 1969
- Tongue
- English
- Weight
- 626 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0010-3640
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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 A local energy decay problem is studied to a typical linear wave equation in an exterior domain. For this purpose, we do not assume any compactness of the support on the initial data. This generalizes a previous famous result due to Morawetz (__Comm. Pure Appl. Math__. 1961; **14**:561β
## Abstract We first construct traveling wave solutions for the SchrΓΆdinger map in β^2^ of the form __m__(__x__~1~, __x__~2~ β Ο΅ __t__), where __m__ has exactly two vortices at approximately $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}(\pm {{1}\over{2 \epsilon}}, 0) \in \R^2$ of degree Β±1. We