Attractors and global averaging of non-autonomous reaction-diffusion equations in R^n
Analysis of PDEs
2007-05-23 v2 Dynamical Systems
Abstract
We consider a family of non-autonomous reaction-diffusion equations with almost periodic, rapidly oscillating principal part and nonlinear interactions. As the frequency of the oscillations tends to infinity, we prove that the solutions of the non-autonomous equations converge to the solutions of the autonomous averaged equation. If the nonlinearity is dissipative, we prove existence of compact attractors and their upper-semicontinuity at infinity.
Keywords
Cite
@article{arxiv.math/0205184,
title = {Attractors and global averaging of non-autonomous reaction-diffusion equations in R^n},
author = {F. Antoci and M. Prizzi},
journal= {arXiv preprint arXiv:math/0205184},
year = {2007}
}
Comments
31 pages; to appear on "Topological Methods in Nonlinear Analysis"; references added