Global Existence Results for a Mathematical Model of Cell Morphogenesis in Calcium-Regulated Strain Fields

The present paper is concerned with the mathematical analysis of a mechano-chemical model describing the dynamics of a cell where calcium input and calcium output processes are involved. In this model the cortical cytoplasm is considered as a (visco)elastic continuum in which calcium ions can diffuse and interact with the cytoskeleton. The evolution of such a medium is described by a nonlinear partial differential equations system, where the balance laws for the concentrations of free calcium and bound (to specific macromolecules) calcium are coupled with the equilibrium equation for the displacement. The existence of a (weak) solution to the corresponding initial-boundary value problem is proved by variational methods. In the strongly viscoelastic case also a uniqueness result is stated. The properties of stationary solutions of the system are discussed.