Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/648067 |
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| _version_ | 1832556592469377024 |
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| author | Yulan Wang Zhaoyin Xiang Jinsong Hu |
| author_facet | Yulan Wang Zhaoyin Xiang Jinsong Hu |
| author_sort | Yulan Wang |
| collection | DOAJ |
| description | We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results. |
| format | Article |
| id | doaj-art-0eed4e8f318c4bc6b337f460e6b6557f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-0eed4e8f318c4bc6b337f460e6b6557f2025-02-03T05:44:52ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/648067648067Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and AbsorptionYulan Wang0Zhaoyin Xiang1Jinsong Hu2School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, ChinaSchool of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, ChinaWe investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.http://dx.doi.org/10.1155/2012/648067 |
| spellingShingle | Yulan Wang Zhaoyin Xiang Jinsong Hu Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption Journal of Applied Mathematics |
| title | Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption |
| title_full | Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption |
| title_fullStr | Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption |
| title_full_unstemmed | Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption |
| title_short | Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption |
| title_sort | blowup analysis for a nonlocal diffusion equation with reaction and absorption |
| url | http://dx.doi.org/10.1155/2012/648067 |
| work_keys_str_mv | AT yulanwang blowupanalysisforanonlocaldiffusionequationwithreactionandabsorption AT zhaoyinxiang blowupanalysisforanonlocaldiffusionequationwithreactionandabsorption AT jinsonghu blowupanalysisforanonlocaldiffusionequationwithreactionandabsorption |