Global Solution to a Model of Tumor Invasion

Abstract. This paper deals with a mathematical model which is used to investigate the role of extracellular matrix (ECM) concentration in tumor cell invasion. The model is a system of partial differential equations governing tumor cell density, the tumor cell-derived protease concentration and the collagen gel concentration. In this system, the equation describing the evolution of the tumor cell density is a diffusion-haptotaxis parabolic equation. For general haptotactic coefficient, the global existence of solutions for this model is proved. The proof is based on a priori estimates, together with the L p estimates and the Schauder estimates of parabolic equations. Mathematics Subject Classification: 22E46; 35R35; 53C3