Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source
This paper deals with the global existence of solutions to a strongly coupled parabolic-parabolic system of chemotaxis arising from the theory of reinforced random walks. More specifically, we investigate the attraction-repulsion chemotaxis model with fast diffusive term and nonlinear source subject...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/143718 |
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| _version_ | 1832565644074156032 |
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| author | Yingjie Zhu Fuzhong Cong |
| author_facet | Yingjie Zhu Fuzhong Cong |
| author_sort | Yingjie Zhu |
| collection | DOAJ |
| description | This paper deals with the global existence of solutions to a strongly coupled parabolic-parabolic system of chemotaxis arising from the theory of reinforced random walks. More specifically, we investigate the attraction-repulsion chemotaxis model with fast diffusive term and nonlinear source subject to the Neumann boundary conditions. Such fast diffusion guarantees the global existence of solutions for any given initial value in a bounded domain. Our main results are based on the method of energy estimates, where the key estimates are obtained by a technique originating from Moser’s iterations. Moreover, we notice that the cell density goes to the maximum value when the diffusion coefficient of the cell density tends to infinity. |
| format | Article |
| id | doaj-art-49362219996e4daa9752faee7de8e848 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-49362219996e4daa9752faee7de8e8482025-02-03T01:07:00ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/143718143718Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear SourceYingjie Zhu0Fuzhong Cong1Institute of Mathematics, Jilin University, Changchun 130012, ChinaInstitute of Mathematics, Jilin University, Changchun 130012, ChinaThis paper deals with the global existence of solutions to a strongly coupled parabolic-parabolic system of chemotaxis arising from the theory of reinforced random walks. More specifically, we investigate the attraction-repulsion chemotaxis model with fast diffusive term and nonlinear source subject to the Neumann boundary conditions. Such fast diffusion guarantees the global existence of solutions for any given initial value in a bounded domain. Our main results are based on the method of energy estimates, where the key estimates are obtained by a technique originating from Moser’s iterations. Moreover, we notice that the cell density goes to the maximum value when the diffusion coefficient of the cell density tends to infinity.http://dx.doi.org/10.1155/2015/143718 |
| spellingShingle | Yingjie Zhu Fuzhong Cong Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source Discrete Dynamics in Nature and Society |
| title | Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source |
| title_full | Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source |
| title_fullStr | Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source |
| title_full_unstemmed | Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source |
| title_short | Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source |
| title_sort | global existence to an attraction repulsion chemotaxis model with fast diffusion and nonlinear source |
| url | http://dx.doi.org/10.1155/2015/143718 |
| work_keys_str_mv | AT yingjiezhu globalexistencetoanattractionrepulsionchemotaxismodelwithfastdiffusionandnonlinearsource AT fuzhongcong globalexistencetoanattractionrepulsionchemotaxismodelwithfastdiffusionandnonlinearsource |