paper

Attractors and global averaging of non-autonomous reaction-diffusion equations in R^n

arXiv:math/0205184

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.

31 pages; to appear on "Topological Methods in Nonlinear Analysis"; references added

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