Well-posedness and Stability of a Multi-dimensional Tumor Growth Model

We study a moving boundary problem modeling the growth of in vitro tumors. This problem consists of two elliptic equations describing the distribution of the nutrient and the internal pressure, respectively, and a first-order partial differential equation describing the evolution of the moving boundary. An important feature is that the effect of surface tension on the moving boundary is taken into account. We show that this problem is locally well-posed for a large class of initial data by using analytic semi-group theory. We also prove that if the surface tension coefficient gamma is larger than a threshold value gamma (*) then the unique flat equilibrium is asymptotically stable, whereas in the case gamma < gamma (*) this flat equilibrium is unstable.