Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant

Tello del Castillo, José Ignacio and Negreanu Pruna, Mihaela (2015). Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant. "Journal of Differential Equations", v. 258 (n. 5); pp. 1592-1617. ISSN 0022-0396. https://doi.org/10.1016/j.jde.2014.11.009.

Description

Title: Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant
Author/s:
  • Tello del Castillo, José Ignacio
  • Negreanu Pruna, Mihaela
Item Type: Article
Título de Revista/Publicación: Journal of Differential Equations
Date: 5 March 2015
ISSN: 0022-0396
Volume: 258
Subjects:
Freetext Keywords: Asymptotic behavior; Stability; Global existence; Chemotaxis
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 the behavior of two biological populations “u” and “v” attracted by the same chemical substance whose behavior is described in terms of second order parabolic equations. The model considers a logistic growth of the species and the interactions between them are relegated to the chemoattractant production. The system is completed with a third equation modeling the evolution of chemical. We assume that the chemical “w” is a non-diffusive substance and satisfies an ODE, more precisely, {ut=Δu−∇⋅(uχ1(w)∇w)+μ1u(1−u),x∈Ω,t>0,vt=Δv−∇⋅(vχ2(w)∇w)+μ2v(1−v),x∈Ω,t>0,wt=h(u,v,w),x∈Ω,t>0, under appropriate boundary and initial conditions in an n-dimensional open and bounded domain Ω. We consider the cases of positive chemo-sensitivities, not necessarily constant elements. The chemical production function h increases as the concentration of the species “u” and “v” increases. We first study the global existence and uniform boundedness of the solutions by using an iterative approach. The asymptotic stability of the homogeneous steady state is a consequence of the growth of h, χi and the size of μi. Finally, some examples of the theoretical results are presented for particular functions h and χi.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2013-42907DGICTUnspecifiedUnspecified

More information

Item ID: 44788
DC Identifier: http://oa.upm.es/44788/
OAI Identifier: oai:oa.upm.es:44788
DOI: 10.1016/j.jde.2014.11.009
Official URL: http://www.sciencedirect.com/science/article/pii/S0022039614004458
Deposited by: Memoria Investigacion
Deposited on: 28 Apr 2017 18:51
Last Modified: 10 Jun 2019 14:07
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