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### Open Access Journals

DCDS

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.

PROC

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.

PROC

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.

## Year of publication

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