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

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)∩L2p−2(Ω) for the nonautonomous dynamical system...

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Main Author: Nguyen Dinh Binh
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/272145
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author Nguyen Dinh Binh
author_facet Nguyen Dinh Binh
author_sort Nguyen Dinh Binh
collection DOAJ
description 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)∩L2p−2(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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spelling doaj-art-e3f0152ed0b345149c857c2bd7edbe0f2025-02-03T05:52:04ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/272145272145Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin OperatorNguyen Dinh Binh0Faculty of Applied Mathematics and Informatics, Hanoi University of Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, VietnamConsidered 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)∩L2p−2(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.http://dx.doi.org/10.1155/2012/272145
spellingShingle Nguyen Dinh Binh
Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator
Abstract and Applied Analysis
title Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator
title_full Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator
title_fullStr Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator
title_full_unstemmed Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator
title_short Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator
title_sort regularity and exponential growth of pullback attractors for semilinear parabolic equations involving the grushin operator
url http://dx.doi.org/10.1155/2012/272145
work_keys_str_mv AT nguyendinhbinh regularityandexponentialgrowthofpullbackattractorsforsemilinearparabolicequationsinvolvingthegrushinoperator