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Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator

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  • Nguyen Dinh Binh

Abstract

Considered here is the first initial boundary value problem for a semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain Ω. We prove the regularity and exponential growth of a pullback attractor in the space S02(Ω)∩L22p−(Ω) for the nonautonomous dynamical system associated to the problem. The obtained results seem to be optimal and, in particular, improve and extend some recent results on pullback attractors for reaction‐diffusion equations in bounded domains.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:272145
DOI: 10.1155/2012/272145
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