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.Since multicellular spheroids are routinely used as in vitro(i.e.,outside live organisms)models of cancer growth and they can be observed and controlled in the laboratory,the following inverse problem is studied:given observed dynamics of tumor growth,a certain parameter is determined.The Lipschitz stability of solutions to the above-mentioned inverse problem is established,and this inverse problem is solved by control theory.Numerical methods for solving the inverse problem are also given.