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Uniform exponential attractors for a singularly perturbed damped wave equation. (English) Zbl 1060.35011
The goal of this paper is to extend the construction of continuous exponential attractors (without time shifts) to singularly perturbed damped wave equations. The difficulty here is based on the fact that the phase spaces for the perturbed and unperturbed equations are not the same (the limit equation being a (parabolic) reaction-diffusion equation).

MSC:
35B25 Singular perturbations in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
37L30 Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents
35B41 Attractors
35L70 Second-order nonlinear hyperbolic equations
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