A free boundary problem arising in biology

Abstract

This work was intended as an attempt to investigate a simple mathematical model cell. This model represents a problem with free boundary for system of two differential equations, one of which is parabolic and another one is elliptic. We apply a method which consists of the following. First, we construct a special system of difference-differential approximating elliptic problems, then we prove some uniform estimates and pass to the limit. We prove the existence of the classical solution.