Attractors for damped quintic wave equations in bounded domains
Abstract
The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2013
- DOI:
- 10.48550/arXiv.1309.6272
- arXiv:
- arXiv:1309.6272
- Bibcode:
- 2013arXiv1309.6272K
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35B40;
- 35B45