Global existence and stability of solution of a reaction-diffusion model for cancer invasion

In this paper, we study a mathematical model of cancer invasion proposed by Gatenby and Gawlinski. The model is a strongly coupled degenerate reaction-diffusion system. Very few mathematical results are known for this system. We investigate the global existence of classical solutions for the system by using energy estimates and the bootstrap arguments, and global asymptotic stability of equilibrium points of the system by Lyapunov functions.