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Issue ESAIM: Proc.
Volume 20, 2007
RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005
Page(s) 129 - 137
DOI http://dx.doi.org/10.1051/proc:072012
Published online 13 October 2007

ESAIM: Proc., 2007, Vol. 20, pp. 129-137
DOI: 10.1051/proc:072012

optimal control for a nonlinear system describing the mechanochemical process in cell morphogenesis

Lahcen Ghannam

Laboratoire MIP-UMR 5640, Université Paul Sabatier, UFR MIG, 118, route de Narbonne, F-31062 Toulouse Cedex 04, FRANCE;

ghannam@cict.fr

(Published online: 13 October 2007)

Abstract
In this paper a system of partial differential equations is considered that constitutes a one-dimensional mechanochemical model of cellular morphogenesis, based on calcium ion regulation of the viscoelastic properties of cellular cortex. Calcium input and out put processes, as well as diffusive effects are accounted in the description of the cell dynamics. The stability behavior under distributed loads and calcium sources at the boundary is investigated. An optimal control problem is formulated which uses loads and calcium sources as control variables. The existence of optimal controls is proved.


Résumé
Cet article est consacré à l'étude du contrôle optimal d'un système parabolique non linéaire qui modèlise la morphogenèse cellulaire. Ce modèle est basé sur l'interaction entre le calcium et les propriétés viscoélastiques du cytoplasme cellulaire. On montre un résultat de continuité par rapport aux données du problème ainsi que l'existence d'un contrôle, sans toutefois expliciter les conditions d'optimalité.


Mathematics Subject Classification. 92C15, 74D10, 35K60, 35D05, 49J20

Key words: Cell morphogenesis, Nonlinear parabolic systems, Global existence, Optimal control


© EDP Sciences, ESAIM 2007


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