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 the paper by 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.
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Masayasu Mimura, Roberta Dal Passo, Michiel Bertsch, A free boundary problem arising in a simpliﬁed tumour growth model of contact inhibition. Interfaces Free Bound. 12 (2010), no. 2, pp. 235–250