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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/5340489 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558244705337344 |
|---|---|
| author | Yongqin Xie Yanan Li Ye Zeng |
| author_facet | Yongqin Xie Yanan Li Ye Zeng |
| author_sort | Yongqin Xie |
| collection | DOAJ |
| 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)). |
| format | Article |
| id | doaj-art-64734ed6c7514afaa1cd44148a7a4ebe |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-64734ed6c7514afaa1cd44148a7a4ebe2025-02-03T01:32:52ZengWileyJournal 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 |
| spellingShingle | Yongqin Xie Yanan Li Ye Zeng Uniform Attractors for Nonclassical Diffusion Equations with Memory Journal of Function Spaces |
| title | 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_short | Uniform Attractors for Nonclassical Diffusion Equations with Memory |
| title_sort | uniform attractors for nonclassical diffusion equations with memory |
| url | http://dx.doi.org/10.1155/2016/5340489 |
| work_keys_str_mv | AT yongqinxie uniformattractorsfornonclassicaldiffusionequationswithmemory AT yananli uniformattractorsfornonclassicaldiffusionequationswithmemory AT yezeng uniformattractorsfornonclassicaldiffusionequationswithmemory |