Qualitative Analysis Of The Solution To A Class Of Mathematical Model For Tumor Cells

Tumor is one of the diseases that threaten human health and safety.Using mathematical methods to study tumor problems is helpful to understand the mechanism of tumor formation and development,which is very helpful for the treatment and precaution of tumor.The mathematical model described by partial differential equation can well fit the growth of tumor and its development,as a consequence,it has great scientific significance and mathematical research value.This paper studies two mathematical models of tumor growth expressed by parabolic partial differential equations,respectively prove the existence of global solutions and the existence and uniqueness of the global solution.The first problem studied in the paper is the metabolic model of colon cancer cells.The model contains five coupled reaction-diffusion equations,in which some equations involve discontinuous terms.By approximating the discontinuous function,then using the L~p-theory for parabolic equations and the Schauder Fixed Point Theorem,it is proved that the approximation problem exists a unique global solution,which finally verify that the original problem exists a global solution.The second problem is the mathematical model of IL-27 induction of anti-tumor T cells response,which is a coupled system of partial differential equations.By applying Banach Fixed Point Theorem and the ~pL-estimate for parabolic equations,it is proved that the problem exists a unique global solution.