A free boundary problem arising in a simplified tumour growth model of contact inhibition

It is observed in vitro and in vivo that when two populations of different types of cells come near to each other, the rate of proliferation of most cells decreases. This phenomenon is often called contact inhibition of growth between two cells. In this paper, we consider a simplified 1-dimensional PDE-model for normal and abnormal cells, motivated by a paper of Chaplain, Graziano and Preziosi. We show that if the two populations are initially segregated, then they remain segregated due to the contact inhibition mechanism. In this case the system of PDE's can be formulated as a free boundary problem.