Infinite energy solutions for critical wave equation with fractional damping in unbounded domains

Savostianov, Anton

Abstract

This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of R3 with fractional damping of the form View the MathML source. The work extends previously known results for bounded domains in finite energy case. Furthermore, well-posedness and existence of locally-compact smooth attractors for the critical quintic non-linearity are obtained under less restrictive assumptions on non-linearity, relaxing some artificial technical conditions used before. This is achieved by virtue of new type Lyapunov functional that allows to establish extra space–time regularity of solutions of Strichartz type

Citation

Savostianov, A. (2016). Infinite energy solutions for critical wave equation with fractional damping in unbounded domains. Nonlinear Analysis: Theory, Methods and Applications, 136, 136-167. https://doi.org/10.1016/j.na.2016.02.016

• Journal Article Type: Article
• Acceptance Date: Feb 16, 2016
• Online Publication Date: Mar 8, 2016
• Publication Date: May 1, 2016
• Deposit Date: Apr 25, 2017
• Publicly Available Date: May 4, 2017
• Journal: Nonlinear Analysis: Theory, Methods and Applications
• Print ISSN: 0362-546X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 136
• Pages: 136-167
• DOI: https://doi.org/10.1016/j.na.2016.02.016
• Public URL: https://durham-repository.worktribe.com/output/1380712
• Related Public URLs: https://arxiv.org/abs/1511.04592