Attractors for Damped Quintic Wave Equations in Bounded Domains

Kalantarov, Varga; Savostianov, Anton; Zelik, Sergey

Abstract

The dissipative wave equation with a critical quintic non-linearity 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.

Citation

Kalantarov, V., Savostianov, A., & Zelik, S. (2016). Attractors for Damped Quintic Wave Equations in Bounded Domains. Annales Henri Poincaré, 17(9), 2555-2584. https://doi.org/10.1007/s00023-016-0480-y

• Journal Article Type: Article
• Acceptance Date: Jan 5, 2016
• Online Publication Date: Apr 7, 2016
• Publication Date: Sep 1, 2016
• Deposit Date: Apr 25, 2017
• Publicly Available Date: May 4, 2017
• Journal: Annales Henri Poincaré
• Print ISSN: 1424-0637
• Electronic ISSN: 1424-0661
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 9
• Pages: 2555-2584
• DOI: https://doi.org/10.1007/s00023-016-0480-y
• Public URL: https://durham-repository.worktribe.com/output/1388796
• Related Public URLs: https://arxiv.org/abs/1309.6272