Analysis of a mathematical model for tumor growth with Gibbs-Thomson relation

In this paper we study a mathematical model for the growth of nonnecrotic solid tumor. The tumor is assumed to be radially symmetric and its radius R(t) is an unknown function of time t as tumor growth, and the model is in the form of a free boundary problem. The feature of the model is that a Gibbs-Thomson relation is taken into account, which results an interesting phenomenon that there exist two stationary solutions (depending on the model parameters). The global existence and uniqueness of solution are established. By denoting c the ratio of the diffusion time scale to the tumor doubling time scale, we prove that for sufficiently small c>0, the stationary solution with the larger radius is asymptotically stable, and the other smaller one is unstable.