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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]
René Dáger1 ; Víctor Navarro2 ; Mihaela Negreanu2 
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, Volume 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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Révisé le :
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DOI : 10.5802/crmath.17
René Dáger 1 ; Víctor Navarro 2 ; Mihaela Negreanu 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
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     language = {en},
}
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René Dáger; Víctor Navarro; Mihaela Negreanu. Uniform boundedness of solutions for a predator-prey system with diffusion and chemotaxis. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 103-108. doi : 10.5802/crmath.17. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.17/

[1] Nicholas D. Alikakos L p bounds of solutions of reaction-diffusion equations, Commun. Partial Differ. Equations, Volume 4 (1979), pp. 827-868 | Zbl

[2] Herbert Amann Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems, Differ. Integral Equ., Volume 3 (1990) no. 1, pp. 13-75 | MR | Zbl

[3] Herbert Amann Nonhomogeneous linear and quasilinear elliptic and parabollic boundary value problems, Function spaces, differential operators and nonlinear analysis (Teubner-Texte zur Mathematik), Volume 133, Teubner, 1993, pp. 9-126 | DOI | Zbl

[4] Masataka Kuwamura Turing instabilities in prey-predator systems with dormancy of predators, J. Math. Biol., Volume 71 (2015) no. 1, pp. 125-149 | DOI | Zbl

[5] Masataka Kuwamura; Takefumi Nakazawa Dormancy of predators dependent on the rate of variation in prey density, SIAM J. Appl. Math., Volume 71 (2011) no. 1, pp. 169-179 | DOI | MR | Zbl

[6] Mihaela Negreanu; J. Ignacio Tello On a two species chemotaxis model with slow chemical diffusion, SIAM J. Math. Anal., Volume 46 (2014) no. 6, pp. 3761-3781 | DOI | MR | Zbl

[7] Mihaela Negreanu; J. Ignacio Tello Global existence and asymptotic behavior of solutions to a Predator-Prey chemotaxis system with two chemicals, J. Math. Anal. Appl., Volume 474 (2019) no. 2, pp. 1116-1131 | DOI | MR | Zbl

[8] Sainan Wu; Junping Shi; Boying Wu Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis, J. Differ. Equations, Volume 260 (2016) no. 7, pp. 5847-5874 | MR | Zbl

[9] Sainan Wu; Jinfeng Wang; Junping Shi Dynamics and pattern formation of a diffusive predator-prey model with predator-taxis, Math. Models Methods Appl. Sci., Volume 28 (2018), pp. 2275-2312 | MR | Zbl

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