Smooth attractors for the quintic wave equations with fractional damping

Article type: Research Article

Authors: Savostianov, Anton | Zelik, Sergey^;

Affiliations: Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK. E-mails: {a.savostianov, s.zelik}@surrey.ac.uk

Note: [] Corresponding author. E-mail: [email protected]

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.

Keywords: damped wave equation, fractional damping, critical nonlinearity, global attractor, smoothness

DOI: 10.3233/ASY-131208

Journal: Asymptotic Analysis, vol. 87, no. 3-4, pp. 191-221, 2014