Abstract
In this paper we prove an existence and uniqueness result for a time-dependent problem related to a mechanochemical model of cellular morphogenesis, based on calcium ion regulation of the viscoelastic properties of the cellular cortex. Calcium input and output processes, as well as diffusive effects, are accounted in the description of the cell dynamics. The resulting system of nonlinear partial differential equations consists of the balance laws for the concentrations of free calcium and bound (to specific macro-molecules) calcium, coupled with the equilibrium equations for the displacements. It is shown that the initial-boundary value problem has only one solution which satisfies suitable boundedness estimates regarding calcium concentrations.
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