The growth and development of solid tumors occurs in two distinct phases： the avascular and the vascular phase. During the former growth phase the tumor remains in a diffusionlimited dormant state of a few millimeters in diameter

while during the later phase

invasion and metastasis do take place. A mathematical model of cancer cell breakout and invasion of normal tissue or extracellular matrix is studied. The model consists of a system of four Reactiondiffusiontaxis partial differential equations and a degenerate parabolic partial differential equations. By using the parabolic Lptheory

the parabolic Schauder estimates

principle of comparison and the Banach fixed point theorem

it is proved that this system has a unique global solution.