Attractors and global averaging of non-autonomous reaction-diffusion equations in Rⁿ

2002/05/16 by F. Antoci, Antoci, F., M. Prizzi +1
Mathematics · #34G20 #35L70 #35Q30 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.DS #msc:34G20 #msc:35L70 #msc:35Q30

paper · pdf · doi:10.48550/arxiv.math/0205184

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

arxiv created 2002/06/17 · arxiv updated 2009/11/30

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.

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