A Weak Comparison Principle for Reaction-Diffusion Systems
We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the cas...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/679465 |
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| _version_ | 1832560338356142080 |
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| author | José Valero |
| author_facet | José Valero |
| author_sort | José Valero |
| collection | DOAJ |
| description | We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞
is proved for at least one solution of the problem. |
| format | Article |
| id | doaj-art-b107fdd2652f4ea6a2c718bd7586c600 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-b107fdd2652f4ea6a2c718bd7586c6002025-02-03T01:27:54ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/679465679465A Weak Comparison Principle for Reaction-Diffusion SystemsJosé Valero0Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avenida Universidad s/n, 03202 Elche, SpainWe prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.http://dx.doi.org/10.1155/2012/679465 |
| spellingShingle | José Valero A Weak Comparison Principle for Reaction-Diffusion Systems Journal of Function Spaces and Applications |
| title | A Weak Comparison Principle for Reaction-Diffusion Systems |
| title_full | A Weak Comparison Principle for Reaction-Diffusion Systems |
| title_fullStr | A Weak Comparison Principle for Reaction-Diffusion Systems |
| title_full_unstemmed | A Weak Comparison Principle for Reaction-Diffusion Systems |
| title_short | A Weak Comparison Principle for Reaction-Diffusion Systems |
| title_sort | weak comparison principle for reaction diffusion systems |
| url | http://dx.doi.org/10.1155/2012/679465 |
| work_keys_str_mv | AT josevalero aweakcomparisonprincipleforreactiondiffusionsystems AT josevalero weakcomparisonprincipleforreactiondiffusionsystems |