On a parabolic-elliptic chemotaxis system with periodic asymptotic behavior

Negreanu, Mihaela and Tello Del Castillo, Jose Ignacio and Manuel Vargas, Antonio (2019). On a parabolic-elliptic chemotaxis system with periodic asymptotic behavior. "Mathematical Methods in the Applied Sciences", v. 42 (n. 4); pp. 1210-1226. ISSN 0170-4214. https://doi.org/10.1002/mma.5423.

Description

Title: On a parabolic-elliptic chemotaxis system with periodic asymptotic behavior
Author/s:
  • Negreanu, Mihaela
  • Tello Del Castillo, Jose Ignacio
  • Manuel Vargas, Antonio
Item Type: Article
Título de Revista/Publicación: Mathematical Methods in the Applied Sciences
Date: 2019
ISSN: 0170-4214
Volume: 42
Subjects:
Freetext Keywords: Parabolic-Elliptic systems of PDEs; Chemotaxis; Asymptotic behavior; Periodic solutions; Sub- and Super-solutions; Rectangle method
Faculty: E.T.S.I. de Sistemas Informáticos (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We study a parabolic‐elliptic chemotactic PDEs system, which describes the evolution of a biological population “u” and a chemical substance “v” in a bounded domain. We consider a growth term of logistic type in the equation of “u” in the form μu(1 − u + f(t,x)). The function “f,” describing the resources of the systems, presents a periodic asymptotic behavior in the sense where f ∗ is independent of x and periodic in time. We study the global existence of solutions and its asymptotic behavior. Under suitable assumptions on the initial data and f ∗, if the constant chemotactic sensitivity χ satisfies we obtain that the solution of the system converges to a homogeneous in space and periodic in time function.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2017-83391-PUnspecifiedUniversidad Politécnica de MadridSistemas no lineales en matemática industrial y otras aplicaciones

More information

Item ID: 67062
DC Identifier: https://oa.upm.es/67062/
OAI Identifier: oai:oa.upm.es:67062
DOI: 10.1002/mma.5423
Official URL: https://onlinelibrary.wiley.com/doi/10.1002/mma.5423
Deposited by: Memoria Investigacion
Deposited on: 08 Mar 2022 13:52
Last Modified: 08 Mar 2022 13:52
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