Mathematical analysis and numerical simulation of free boundary problem modeling tumor evolution

In this paper, we consider a free boundary problem that arises in the mathematical modeling of cancer. In this model, a parameter η is introduced to represent the killing rate of cancer cells by the T cells. We study the existence of steady state solution to the free boundary problem and its linear stability when the parameter η satisfies certain conditions. The uniqueness and existence of the global solution to the model are then discussed and properties of the solution are also obtained. We derive a finite difference algorithm for the problem and analyze the stability of the algorithm. Finally we perform numerical simulations to validate the theoretical results.