Abstract
This chapter presents the study of the mathematical analysis, the controllability and a numerical simulation for a simple, avascular model of growth of a tumor. It describes the biological phenomenology of several processes, which influence the growth and development of tumors. The mathematical modelling is presented by describing different models of partial differential equations (PDE). The chapter presents the proofs of the solvability of the model equations and discusses the uniqueness of solutions under additional conditions. It discusses the controllability of the growth of the tumor by a localized internal action of the inhibitor on a nonnecrotic tumor. It is obvious that this type of results has merely a mathematical interest and it does not suggest any special therapeutical strategy to inhibit tumor growth. Nevertheless the results show that there is not any obstruction to the controllability (as it appears, for instance, in some similar PDE's models). The chapter addresses the numerical simulation of the problem.
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