Mathematical analysis of a model of chemotaxis arising from morphogenesis

Tello del Castillo, José Ignacio and Stinner, Christian and Winkler, Michael (2012). Mathematical analysis of a model of chemotaxis arising from morphogenesis. "Mathematical Methods in the Applied Sciences", v. 35 (n. 4); pp. 445-465. ISSN 0170-4214. https://doi.org/10.1002/mma.1573.

Description

Title: Mathematical analysis of a model of chemotaxis arising from morphogenesis
Author/s:
  • Tello del Castillo, José Ignacio
  • Stinner, Christian
  • Winkler, Michael
Item Type: Article
Título de Revista/Publicación: Mathematical Methods in the Applied Sciences
Date: 15 March 2012
ISSN: 0170-4214
Volume: 35
Subjects:
Freetext Keywords: chemotaxis, global existence, boundedness, stability, steady states, quimiotaxis, existencia global, límites, estabilidad, estados estacionarios.
Faculty: E.U. de Informática (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

More information

Item ID: 15745
DC Identifier: http://oa.upm.es/15745/
OAI Identifier: oai:oa.upm.es:15745
DOI: 10.1002/mma.1573
Official URL: http://onlinelibrary.wiley.com/doi/10.1002/mma.v35.4/issuetoc
Deposited by: Memoria Investigacion
Deposited on: 12 Jun 2013 14:32
Last Modified: 21 Apr 2016 16:02
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