GLOBAL SOLUTION TO A MODEL FOR CELL MORPHOGENESIS BY CALCIUM-REGULATED STRAIN FIELDS

In this paper we prove an existence and uniqueness result for a time-d ependent problem related to a mechanochemical model of cellular morpho genesis, based on calcium ion regulation of the viscoelastic propertie s of the cellular cortex. Calcium input and output processes, as well as diffusive effects, are accounted in the description of the cell dyn amics. The resulting system of nonlinear partial differential equation s consists of the balance laws for the concentrations of free calcium and bound (to specific macro-molecules calcium, coupled with the equil ibrium equations for the displacements. It is shown that the initial-b oundary value problem has only one solution which satisfies suitable b oundedness estimates regarding calcium concentrations.