On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity

Tello del Castillo, José Ignacio and Negreanu, Mihaela (2013). On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity. "Nonlinear Analysis: Theory, Methods & Applications", v. 80 (n. null); pp. 1-13. ISSN 0362-546X. https://doi.org/10.1016/j.na.2012.12.004.

Description

Title: On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity
Author/s:
  • Tello del Castillo, José Ignacio
  • Negreanu, Mihaela
Item Type: Article
Título de Revista/Publicación: Nonlinear Analysis: Theory, Methods & Applications
Date: March 2013
ISSN: 0362-546X
Volume: 80
Subjects:
Freetext Keywords: Chemotaxis; Asymptotic behavior; Stability of solutions
Faculty: E.U. de Informática (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 system describing the evolution of a population’s density “u” and a chemoattractant’s concentration “v”. The system considers a non-constant chemotactic sensitivity given by “χ(N−u)”, for N≥0, and a source term of logistic type “λu(1−u)”. The existence of global bounded classical solutions is proved for any χ>0, N≥0 and λ≥0. By using a comparison argument we analyze the stability of the constant steady state u=1, v=1, for a range of parameters. – For N>1 and Nλ>2χ, any positive and bounded solution converges to the steady state. – For N≤1 the steady state is locally asymptotically stable and for χN<λ, the steady state is globally asymptotically stable.

More information

Item ID: 33253
DC Identifier: http://oa.upm.es/33253/
OAI Identifier: oai:oa.upm.es:33253
DOI: 10.1016/j.na.2012.12.004
Official URL: http://www.sciencedirect.com/science/article/pii/S0362546X12004567
Deposited by: Memoria Investigacion
Deposited on: 24 Apr 2015 18:42
Last Modified: 24 Apr 2015 18:42
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