Global Solution To A Model Of Tumor Invasion

This paper deal 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 cellderived 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 for the model is proved.The proof is based on a priori estimates,together with the L~p estimates and the Schauder estimates of parabolic equations.Finally,we consider a nonlinear model,after some transforms we prove the local existence for this new model.