Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model
Volume 86 / 2009
Abstract
In the present paper, we consider an approximate system of one-dimensional simplified tumor invasion model, which was originally proposed by Chaplain and Anderson in \cite{chaplain-anderson-03}. The simplified tumor invasion model is composed of PDE and ODE. Actually, the PDE is the balance equation of the density of tumor cells and the ODE describes the dynamics of concentration of extracellular matrix. In this model, we take into account that the random motility of the density of tumor cells is given by a function of space and time, that is, it is not a positive constant. Moreover, the PDE contains a (nonlinear) function which describes the proliferation as well as the apoptosis of tumor cells. Our main objective is to give the local existence and uniqueness of the solutions to the approximate system.
