Existence of Solutions for a Quasilinear Reaction Diffusion System
The degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. This paper is extended the existence of solutions from the quasimonotone reaction functions (e.g., inhibitor-inhibitor mechanism) to the mixed quasimonotone reaction functions (e.g., activato...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/368425 |
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| _version_ | 1832550041937510400 |
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| author | Canrong Tian |
| author_facet | Canrong Tian |
| author_sort | Canrong Tian |
| collection | DOAJ |
| description | The degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. This paper is extended the existence of solutions from the quasimonotone reaction functions (e.g., inhibitor-inhibitor mechanism) to the mixed quasimonotone reaction functions (e.g., activator-inhibitor mechanism). By Schauder fixed point theorem, it is shown that the system admits at least one positive solution if there exist a coupled of upper and lower solutions. This result is applied to a Lotka-Volterra predator-prey model. |
| format | Article |
| id | doaj-art-ff1243ef72b541dd8824b89de13c06fb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ff1243ef72b541dd8824b89de13c06fb2025-02-03T06:08:02ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/368425368425Existence of Solutions for a Quasilinear Reaction Diffusion SystemCanrong Tian0Department of Basic Sciences, Yancheng Institute of Technology, Jiangsu, Yancheng 224003, ChinaThe degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. This paper is extended the existence of solutions from the quasimonotone reaction functions (e.g., inhibitor-inhibitor mechanism) to the mixed quasimonotone reaction functions (e.g., activator-inhibitor mechanism). By Schauder fixed point theorem, it is shown that the system admits at least one positive solution if there exist a coupled of upper and lower solutions. This result is applied to a Lotka-Volterra predator-prey model.http://dx.doi.org/10.1155/2012/368425 |
| spellingShingle | Canrong Tian Existence of Solutions for a Quasilinear Reaction Diffusion System Abstract and Applied Analysis |
| title | Existence of Solutions for a Quasilinear Reaction Diffusion System |
| title_full | Existence of Solutions for a Quasilinear Reaction Diffusion System |
| title_fullStr | Existence of Solutions for a Quasilinear Reaction Diffusion System |
| title_full_unstemmed | Existence of Solutions for a Quasilinear Reaction Diffusion System |
| title_short | Existence of Solutions for a Quasilinear Reaction Diffusion System |
| title_sort | existence of solutions for a quasilinear reaction diffusion system |
| url | http://dx.doi.org/10.1155/2012/368425 |
| work_keys_str_mv | AT canrongtian existenceofsolutionsforaquasilinearreactiondiffusionsystem |