Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis
In this Note we study a nonlinear system of reaction-diffusion differential equations consisting of an ordinary differential equation coupled to a fully parabolic chemotaxis system. This system constitutes a mathematical model for the evolution of a prey-predator biological population with chemotaxi...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2020-03-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.17/ |
| _version_ | 1797651540518895616 |
|---|---|
| author | Dáger, René Navarro, Víctor Negreanu, Mihaela |
| author_facet | Dáger, René Navarro, Víctor Negreanu, Mihaela |
| author_sort | Dáger, René |
| collection | DOAJ |
| description | In this Note we study a nonlinear system of reaction-diffusion differential equations consisting of an ordinary differential equation coupled to a fully parabolic chemotaxis system. This system constitutes a mathematical model for the evolution of a prey-predator biological population with chemotaxis and dormant predators. Under suitable assumptions we prove the global in time existence and boundedness of classical solutions of this system in any space dimension. |
| first_indexed | 2024-03-11T16:17:16Z |
| format | Article |
| id | doaj.art-6a85e291ea684655a264a5e2fc1e3972 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:16Z |
| publishDate | 2020-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-6a85e291ea684655a264a5e2fc1e39722023-10-24T14:19:10ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692020-03-01358110310810.5802/crmath.1710.5802/crmath.17Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxisDáger, René0Navarro, Víctor1Negreanu, Mihaela2https://orcid.org/0000-0003-0533-3464Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, SpainDepartamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, SpainDepartamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, SpainIn this Note we study a nonlinear system of reaction-diffusion differential equations consisting of an ordinary differential equation coupled to a fully parabolic chemotaxis system. This system constitutes a mathematical model for the evolution of a prey-predator biological population with chemotaxis and dormant predators. Under suitable assumptions we prove the global in time existence and boundedness of classical solutions of this system in any space dimension.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.17/ |
| spellingShingle | Dáger, René Navarro, Víctor Negreanu, Mihaela Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis Comptes Rendus. Mathématique |
| title | Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis |
| title_full | Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis |
| title_fullStr | Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis |
| title_full_unstemmed | Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis |
| title_short | Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis |
| title_sort | uniform boundedness of solutions for a predator prey system with diffusion and chemotaxis |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.17/ |
| work_keys_str_mv | AT dagerrene uniformboundednessofsolutionsforapredatorpreysystemwithdiffusionandchemotaxis AT navarrovictor uniformboundednessofsolutionsforapredatorpreysystemwithdiffusionandchemotaxis AT negreanumihaela uniformboundednessofsolutionsforapredatorpreysystemwithdiffusionandchemotaxis |