Qualitative Analysis Of A Mathematical Model Of Prostate Tumor Growth

This paper extends Ja.ckson's model describing the growth of a prostate tumor by considering the inequality of random motility coefficients of the androgen-dependent(AD)tumor cells and androgen-independent(AI)ones.The mathematical model rep-resents a free-boundary problem for a nonlinear system of parabolic equations,which describe the evolution of the populations of the above two types of tunmor cells.Under the assumption of radially symmetric,a rigorous mathermatical analysis of this model is given.The local existence and uniqueness of solutions to the model is proved by using the contraction mapping principle,along with the methods of' sup-and sub-solutions and the parabolic Lp-theory,and the global existence and uniqueness of solutions is proved by using continuation method.