Uniform exponential attractors for a singularly perturbed damped wave equation
Pierre Fabrie - Université Bordeaux-I, Mathématiques Appliquées, 351 Cours de la Libération, 33405 Talence Cedex, France (email)
Abstract: Our aim in this article is to construct exponential attractors for singularly perturbed damped wave equations that are continuous with respect to the perturbation parameter. The main difficulty comes from the fact that the phase spaces for the perturbed and unperturbed equations are not the same; indeed, the limit equation is a (parabolic) reaction-diffusion equation. Therefore, previous constructions obtained for parabolic systems cannot be applied and have to be adapted. In particular, this necessitates a study of the time boundary layer in order to estimate the difference of solutions between the perturbed and unperturbed equations. We note that the continuity is obtained without time shifts that have been used in previous results.
Keywords: Singularly perturbed damped wave equations, reaction-diﬀusion equations,uniform exponential attractors, time boundary layer.
Received: November 2001; Revised: March 2003; Published: October 2003.
2011 Impact Factor.913