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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/272145 |
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| _version_ | 1832554259446497280 |
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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. |
| format | Article |
| id | doaj-art-e3f0152ed0b345149c857c2bd7edbe0f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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 |