Global Existence Solution For The Growth Mathematical Model Of Monolayer Tumor Cells In Vitro

In this paper, two free boundary problems of partial differential equations are studied. We proved that two problems exist global solution respectively. These two models describe the change of the interaction between tumor cells under different conditions.The first chapter is the introduction which has three sections. The first section introduces the research background and significance. The second section expounds the current situation of the research, and the third section introduces some lemma and symbols.In the second chapter, according to the mathematical model of monolayer tumor cells growth in vitro which is established by Helen-Byrne, we explore the situation of model when the tumor cell density is constant to 1. At the same time, the model is a free boundary problem of elliptic partial differential equation with discontinuous term. Therefore, by using approximation method, elliptic Schauder fixed point theorem and the elliptic Lp estimate, we prove that there exists a global solution for this problem.In the final chapter, we explore the situation of model when the tumor cell density n is variable. And at the same time, the researched model is a free boundary problem of parabolic partial differential equation problem with discontinuous term also. Therefore, by using approximation method, parabolic Schauder fixed point theorem and the parabolic Lp estimate, we prove that the problem has a global solution.