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

Savostianov, Anton

doi:10.1016/j.na.2016.02.016

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

Savostianov, Anton

Authors

Anton Savostianov

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
Related Public URLs	https://arxiv.org/abs/1511.04592

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http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
© 2016 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/