DCDS
Uniform exponential attractors for a singularly perturbed damped wave equation
Pierre Fabrie Cedric Galusinski A. Miranville Sergey Zelik
Discrete & Continuous Dynamical Systems - A 2004, 10(1&2): 211-238 doi: 10.3934/dcds.2004.10.211
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: reaction-diffusion equations time boundary layer. Singularly perturbed damped wave equations uniform exponential attractors
PROC
Uniform Gevrey regularity for the attractor of a damped wave equation
Cedric Galusinski Serguei Zelik
Conference Publications 2003, 2003(Special): 305-312 doi: 10.3934/proc.2003.2003.305
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.
keywords: damped wave equation Gevrey regularity partially dissipative. asymptotic behavior exponential attractors
PROC
Water-gas flow in porous media
Cedric Galusinski Mazen Saad
Conference Publications 2005, 2005(Special): 307-316 doi: 10.3934/proc.2005.2005.307
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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