Time evolution for a model of epidermis growth

In this paper, we study a system of nonlinear hyperbolic equations, with nonlocal boundary conditions and a free boundary, arising in the modeling of epidermis growth. The model was introduced in a previous paper (Gandolfi et al. in J Math Biol 62(1):111-141, 2010) where conditions for the existence of a steady state were investigated. The present paper is devoted to prove existence and uniqueness of a solution to the evolution problem and of the related moving boundary representing the external surface of the epidermis. The proof of the theorem is based on the integration along characteristic curves in order to obtain suitable estimates allowing to set up a fixed point procedure. The modellistic aim of the paper is a description of the structure of the epidermis as a layered aggregate of different type of cells.