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

Lahcen Ghannam, Mohammed-Najib Benbourhim, Patrick Chenin, Abdelhak Hassouni, Jean-Baptiste Hiriart-Urruty
2007 ESAIM: Proceedings and Surveys  
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
more » ... which uses loads and calcium sources as control variables. The existence of optimal controls is proved. Résumé Cet article est consacréà l'étude du contrôle optimal d'un système parabolique non linéaire qui modélise 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.
doi:10.1051/proc:072012 fatcat:j73ts5e3ife5dizc3wqshclk4u