LAUSR

In this paper we study a free boundary problem for the growth of multi-layer tumours in the necrotic phase. The tumour region is strip-like and divided into a necrotic region and a proliferating region with two free boundaries. The upper free boundary is the tumour surface and is governed by a Stefan condition. The lower free boundary is the interface separating the necrotic region from the proliferating region, and its evolution is implicit and intrinsically governed by an obstacle problem. By the Nash–Moser implicit function theorem we show that the lower free boundary is smoothly dependent on the upper free boundary, and by using analytic semigroups theory we obtain asymptotic stability of the unique flat stationary solution.