  In this paper we study a free boundary problem for the growth of multi-layer
tumors in necrotic phase. The tumor region is strip-like and divided into
necrotic region and proliferating region with two free boundaries. The upper
free boundary is tumor surface and governed by a Stefan condition. The lower
free boundary is the interface separating necrotic region from proliferating
region, its evolution is implicit and intrinsically governed by an obstacle
problem. We prove that the problem has a unique flat stationary solution, and
there exists a positive constant $\gamma_*$, such that the flat stationary
solution is asymptotically stable for cell-to-cell adhesiveness
$\gamma>\gamma_*$, and unstable for $0<\gamma<\gamma_*$.
