An Inverse Problem Of A Tumor Model

This paper considers a model for the growth of a solid tumor with a single anticancer agent application. The model is a free boundary problem of a nonlinear reaction-diffusion-advection equation, where the free boundary is the surface of the tumor .The global existence of solutions to this model is proved by a fixed point argument. Since multicellular spheroids are routinely used as in vitro models of cancer growth and they can be observed and controlled in the laboratory, in this paper we also study the following inverse problem: Given observed dynamics of tumor growth, we determine a certain parameter.The Lipschitz stability of solutions to above inverse problem is established, and this inverse problem is solved by control theory. Numerical methods for solving the inverse problem are also given.