Existence and Uniqueness of a Chemotaxis System Influenced by Cancer Cells

Abstract

We present a mathematical analysis of a reaction-diffusion model in a bounded open domain which describes vascular endothelial growth factor(VEGF), endothelial cells and oxygen. We use the parabolic theory to prove the existence of the solution in the function space under the homogeneous Neumann conditions. Then we get the existence of nonnegative solution in by using the global Schauder estimation.