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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.
The goal of this paper is to prove time-asymptotic regularity in Gevrey spaces of the solution of a singularly perturbed damped wave equation and to obtain the uniform (with respect to the perturbation parameter) bounds for the associated global and exponential attractors in the appropriate Gervey spaces.
The goal of this paper is to establish a global existence theorem for a strongly degenerate problem modeling water-gas flows mixing compressible and incompressible fluids. The problem is strongly nonlinear and an evolution term degenerates as well as a diffusion term.
keywords: Degenerate problem.
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