Exponential attractors for singularly perturbed damped wave equations: A simple construction

Article type: Research Article

Authors: Miranville, Alain | Pata, Vittorino | Zelik, Sergey

Affiliations: Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086, SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, 86962 Chasseneuil Futuroscope Cedex, France E-mail: miranv@math.univ-poitiers.fr | Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy E-mail: vittorino.pata@polimi.it | Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom E-mail: S.Zelik@surrey.ac.uk

Abstract: This note is concerned with the damped wave equation ε2∂ttu+∂tu−Δu+f(u)=g depending on a small parameter ε and with the corresponding parabolic equation ∂tu−Δu+f(u)=g obtained in the singular limit ε→0. The existence of a family ℳε of exponential attractors which is Hölder continuous with respect to ε is proved.

Keywords: exponential attractors, damped wave equation, singular perturbation, Hölder continuity

Journal: Asymptotic Analysis, vol. 53, no. 1-2, pp. 1-12, 2007