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oai:oa.upm.es:15745
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Mathematical analysis of a model of chemotaxis arising from morphogenesis
Tello del Castillo, JosÃ© Ignacio
Stinner, Christian
Winkler, Michael
Mathematics
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.
E.U. de InformÃ¡tica (UPM)
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
2012-03-15
info:eu-repo/semantics/article
Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 2012-03-15, Vol. 35, No. 4
PeerReviewed
application/pdf
eng
http://onlinelibrary.wiley.com/doi/10.1002/mma.v35.4/issuetoc
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/altIdentifier/doi/10.1002/mma.1573
http://oa.upm.es/15745/