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Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis
[Limite uniforme des solutions pour un système prédateur-proie avec diffusion et chimiotaxie]
Dáger, René1 ; Navarro, Víctor2 ; Negreanu, Mihaela2 
1 Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain
2 Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 103-108.

Dans cette Note, nous étudions un système non linéaire d’équations différentielles partielles de type réaction-diffusion décrivant l’évolution d’un système biologique proie-prédateur avec chimiotaxie et prédateurs dormants. Nous considérons une équation ordinaire couplée à un système parabolique de chimiotaxie. Sous certaines hypothèses appropriées, nous obtenons l’existence globale en temps de solutions classiques du système considéré dans n’importe quelle dimension spatiale.

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.

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DOI : 10.5802/crmath.17
Dáger, René 1 ; Navarro, Víctor 2 ; Negreanu, Mihaela 2

1 Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain
2 Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain 
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     title = {Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {103--108},
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Dáger, René; Navarro, Víctor; Negreanu, Mihaela. Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis. Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 103-108. doi : 10.5802/crmath.17. http://www.numdam.org/articles/10.5802/crmath.17/

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