Global Bounded Classical Solutions for a Gradient-Driven Mathematical Model of Antiangiogenesis in Tumor Growth

Abstract

In this paper, we consider a gradient-driven mathematical model of antiangiogenesis in tumor growth. In the model, the movement of endothelial cells is governed by diffusion of themselves and chemotaxis in response to gradients of tumor angiogenic factors and angiostatin. The concentration of tumor angiogenic factors and angiostatin is assumed to diffuse and decay. The resulting system consists of three parabolic partial differential equations. In the present paper, we study the global existence and boundedness of classical solutions of the system under homogeneous Neumann boundary conditions.