Uniform Attractors for Nonclassical Diffusion Equations with Memory
We introduce a new method (or technique), asymptotic contractive method, to verify uniform asymptotic compactness of a family of processes. After that, the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved u...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/5340489 |
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doaj-64734ed6c7514afaa1cd44148a7a4ebe2020-11-24T23:31:27ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/53404895340489Uniform Attractors for Nonclassical Diffusion Equations with MemoryYongqin Xie0Yanan Li1Ye Zeng2School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, ChinaSchool of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, ChinaSchool of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, ChinaWe introduce a new method (or technique), asymptotic contractive method, to verify uniform asymptotic compactness of a family of processes. After that, the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved under the following conditions: the nonlinearity f satisfies the polynomial growth of arbitrary order and the time-dependent forcing term g is only translation-bounded in Lloc2(R;L2(Ω)).http://dx.doi.org/10.1155/2016/5340489 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yongqin Xie Yanan Li Ye Zeng |
| spellingShingle |
Yongqin Xie Yanan Li Ye Zeng Uniform Attractors for Nonclassical Diffusion Equations with Memory Journal of Function Spaces |
| author_facet |
Yongqin Xie Yanan Li Ye Zeng |
| author_sort |
Yongqin Xie |
| title |
Uniform Attractors for Nonclassical Diffusion Equations with Memory |
| title_short |
Uniform Attractors for Nonclassical Diffusion Equations with Memory |
| title_full |
Uniform Attractors for Nonclassical Diffusion Equations with Memory |
| title_fullStr |
Uniform Attractors for Nonclassical Diffusion Equations with Memory |
| title_full_unstemmed |
Uniform Attractors for Nonclassical Diffusion Equations with Memory |
| title_sort |
uniform attractors for nonclassical diffusion equations with memory |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2016-01-01 |
| description |
We introduce a new method (or technique), asymptotic contractive method, to verify uniform asymptotic compactness of a family of processes. After that, the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved under the following conditions: the nonlinearity f satisfies the polynomial growth of arbitrary order and the time-dependent forcing term g is only translation-bounded in Lloc2(R;L2(Ω)). |
| url |
http://dx.doi.org/10.1155/2016/5340489 |
| work_keys_str_mv |
AT yongqinxie uniformattractorsfornonclassicaldiffusionequationswithmemory AT yananli uniformattractorsfornonclassicaldiffusionequationswithmemory AT yezeng uniformattractorsfornonclassicaldiffusionequationswithmemory |
| _version_ |
1725537991951122432 |