Uniform exponential attractors for a singularly perturbed damped wave equation | Zendy

Pierre Fabrie | Zendy; Cédric Galusinski | Zendy; Alain Miranville | Zendy; Sergey Zelik | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Uniform exponential attractors for a singularly perturbed damped wave equation

Author(s) -

Pierre Fabrie,

Cédric Galusinski,

Alain Miranville,

Sergey Zelik

Publication year - 2003

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2004.10.211

Subject(s) - attractor , damped wave , mathematical analysis , singular perturbation , exponential function , perturbation (astronomy) , mathematics , wave equation , parabolic partial differential equation , exponential decay , reaction–diffusion system , limit (mathematics) , exponential growth , physics , differential equation , quantum mechanics , nuclear physics

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 content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research