On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term
We consider the existence and properties of the global attractor for a class of reaction-diffusion equation ∂u/∂t-Δu-u+κ(x)|u|p-2u+f(u)=0, in Rn×R+; u(x,0)=u0(x), in Rn. Under some suitable assumptions, we first prove that the problem has a global attractor A in L2(Rn). Then, by using the Z2-in...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/251614 |
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| _version_ | 1832568298399596544 |
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| author | Jin Zhang Chengkui Zhong |
| author_facet | Jin Zhang Chengkui Zhong |
| author_sort | Jin Zhang |
| collection | DOAJ |
| description | We consider the existence and properties of the global attractor for a class of reaction-diffusion equation ∂u/∂t-Δu-u+κ(x)|u|p-2u+f(u)=0, in Rn×R+; u(x,0)=u0(x), in Rn. Under some suitable assumptions, we first prove that the problem has a global attractor A in L2(Rn). Then, by using the Z2-index theory, we verify that A is an infinite dimensional set and it contains infinite distinct pairs of equilibrium points. |
| format | Article |
| id | doaj-art-7f45407efe1f4b8abb0bbdffc5343acb |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-7f45407efe1f4b8abb0bbdffc5343acb2025-02-03T00:59:21ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/251614251614On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted TermJin Zhang0Chengkui Zhong1Department of Mathematics, College of Science, Hohai University, Nanjing 210098, ChinaDepartment of Mathematics, Nanjing University, Nanjing 210093, ChinaWe consider the existence and properties of the global attractor for a class of reaction-diffusion equation ∂u/∂t-Δu-u+κ(x)|u|p-2u+f(u)=0, in Rn×R+; u(x,0)=u0(x), in Rn. Under some suitable assumptions, we first prove that the problem has a global attractor A in L2(Rn). Then, by using the Z2-index theory, we verify that A is an infinite dimensional set and it contains infinite distinct pairs of equilibrium points.http://dx.doi.org/10.1155/2015/251614 |
| spellingShingle | Jin Zhang Chengkui Zhong On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term Discrete Dynamics in Nature and Society |
| title | On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term |
| title_full | On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term |
| title_fullStr | On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term |
| title_full_unstemmed | On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term |
| title_short | On Global Attractors for a Class of Reaction-Diffusion Equations on Unbounded Domains with Some Strongly Nonlinear Weighted Term |
| title_sort | on global attractors for a class of reaction diffusion equations on unbounded domains with some strongly nonlinear weighted term |
| url | http://dx.doi.org/10.1155/2015/251614 |
| work_keys_str_mv | AT jinzhang onglobalattractorsforaclassofreactiondiffusionequationsonunboundeddomainswithsomestronglynonlinearweightedterm AT chengkuizhong onglobalattractorsforaclassofreactiondiffusionequationsonunboundeddomainswithsomestronglynonlinearweightedterm |