Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay
We study a very general class of delayed reaction-diffusion equations in which the reaction term can be nonmonotone and spatially nonlocal. By using a fluctuation method, combined with the careful analysis of the corresponding characteristic equations, we obtain some sufficient conditions for the gl...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/378172 |
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| _version_ | 1832563942475431936 |
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| author | Yueding Yuan Zhiming Guo |
| author_facet | Yueding Yuan Zhiming Guo |
| author_sort | Yueding Yuan |
| collection | DOAJ |
| description | We study a very general class of delayed reaction-diffusion equations in which the reaction term can be nonmonotone and spatially nonlocal. By using a fluctuation method, combined with the careful analysis of the corresponding characteristic equations, we obtain some sufficient conditions for the global asymptotic stability of the trivial solution and the positive steady state to the equations subject to the Neumann boundary condition. |
| format | Article |
| id | doaj-art-d331c2c0b9e5461ea26d9c53fc1ae085 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d331c2c0b9e5461ea26d9c53fc1ae0852025-02-03T01:12:13ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/378172378172Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time DelayYueding Yuan0Zhiming Guo1School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, ChinaWe study a very general class of delayed reaction-diffusion equations in which the reaction term can be nonmonotone and spatially nonlocal. By using a fluctuation method, combined with the careful analysis of the corresponding characteristic equations, we obtain some sufficient conditions for the global asymptotic stability of the trivial solution and the positive steady state to the equations subject to the Neumann boundary condition.http://dx.doi.org/10.1155/2014/378172 |
| spellingShingle | Yueding Yuan Zhiming Guo Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay Abstract and Applied Analysis |
| title | Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay |
| title_full | Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay |
| title_fullStr | Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay |
| title_full_unstemmed | Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay |
| title_short | Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay |
| title_sort | global asymptotic stability in a class of reaction diffusion equations with time delay |
| url | http://dx.doi.org/10.1155/2014/378172 |
| work_keys_str_mv | AT yuedingyuan globalasymptoticstabilityinaclassofreactiondiffusionequationswithtimedelay AT zhimingguo globalasymptoticstabilityinaclassofreactiondiffusionequationswithtimedelay |