Mathematical analysis of a model of chemotaxis arising from morphogenesis
In: Mathematical Methods in the Applied Sciences, Jg. 35 (2012-03-15), Heft 4, S. 445-465
Online
serialPeriodical
Zugriff:
We consider non‐negative solution couples (u,v) of ut=uxx−χuvvxx−λu,vt=1−v+u,with positive parameters χand λ, where the spatial domain is the interval (0,1). This system appears as a limit case of a model for morphogenesis 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 χis small and λis large enough.
Titel: |
Mathematical analysis of a model of chemotaxis arising from morphogenesis
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Autor/in / Beteiligte Person: | Stinner, Christian ; Tello, J. Ignacio ; Winkler, Michael |
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Zeitschrift: | Mathematical Methods in the Applied Sciences, Jg. 35 (2012-03-15), Heft 4, S. 445-465 |
Veröffentlichung: | 2012 |
Medientyp: | serialPeriodical |
ISSN: | 0170-4214 (print) ; 1099-1476 (print) |
DOI: | 10.1002/mma.1573 |
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