Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional Response
The stability of a reaction advection diffusion equation with nonlinear-nonlocal functional response is concerned. By using the technical weighted energy method and the comparison principle, the exponential stability of all noncritical traveling waves of the equation can be obtained. Moreover, we ge...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/4614925 |
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| _version_ | 1850175970079670272 |
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| author | Rui Yan Guirong Liu |
| author_facet | Rui Yan Guirong Liu |
| author_sort | Rui Yan |
| collection | DOAJ |
| description | The stability of a reaction advection diffusion equation with nonlinear-nonlocal functional response is concerned. By using the technical weighted energy method and the comparison principle, the exponential stability of all noncritical traveling waves of the equation can be obtained. Moreover, we get the rates of convergence. Our results improve the previous ones. At last, we apply the stability result to some real models, such as an epidemic model and a population dynamic model. |
| format | Article |
| id | doaj-art-baaefd56234e4cbcbeb9159433e7afc8 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-baaefd56234e4cbcbeb9159433e7afc82025-08-20T02:19:21ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/46149254614925Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional ResponseRui Yan0Guirong Liu1School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaThe stability of a reaction advection diffusion equation with nonlinear-nonlocal functional response is concerned. By using the technical weighted energy method and the comparison principle, the exponential stability of all noncritical traveling waves of the equation can be obtained. Moreover, we get the rates of convergence. Our results improve the previous ones. At last, we apply the stability result to some real models, such as an epidemic model and a population dynamic model.http://dx.doi.org/10.1155/2017/4614925 |
| spellingShingle | Rui Yan Guirong Liu Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional Response Discrete Dynamics in Nature and Society |
| title | Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional Response |
| title_full | Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional Response |
| title_fullStr | Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional Response |
| title_full_unstemmed | Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional Response |
| title_short | Exponential Stability of Traveling Waves for a Reaction Advection Diffusion Equation with Nonlinear-Nonlocal Functional Response |
| title_sort | exponential stability of traveling waves for a reaction advection diffusion equation with nonlinear nonlocal functional response |
| url | http://dx.doi.org/10.1155/2017/4614925 |
| work_keys_str_mv | AT ruiyan exponentialstabilityoftravelingwavesforareactionadvectiondiffusionequationwithnonlinearnonlocalfunctionalresponse AT guirongliu exponentialstabilityoftravelingwavesforareactionadvectiondiffusionequationwithnonlinearnonlocalfunctionalresponse |