Smooth attractors for the quintic wave equations with fractional damping

Savostianov, Anton; Zelik, Sergey

Abstract

Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.

Citation

Savostianov, A., & Zelik, S. (2014). Smooth attractors for the quintic wave equations with fractional damping. Asymptotic Analysis, 87(3-4), 191-221. https://doi.org/10.3233/asy-131208

• Journal Article Type: Article
• Publication Date: Jan 1, 2014
• Deposit Date: Apr 25, 2017
• Publicly Available Date: Aug 15, 2017
• Journal: Asymptotic Analysis
• Print ISSN: 0921-7134
• Electronic ISSN: 1875-8576
• Publisher: IOS Press
• Peer Reviewed: Peer Reviewed
• Volume: 87
• Issue: 3-4
• Pages: 191-221
• DOI: https://doi.org/10.3233/asy-131208
• Public URL: https://durham-repository.worktribe.com/output/1360097
• Related Public URLs: https://arxiv.org/abs/1306.2294