Global Mild Solution for a Chemotaxis-Haptotaxis Model of Tumor Invasion

This paper deals with a mathematical model of tumor invasion developed by Chaplain and Lolas. Besides random motion, the tumor cells are directed not only by haptotaxis (cellular locomotion directed in response to a concentration gradient of adhesive molecules along extracellular matrix) but also by chemotaxis (cellular locomotion directed in response to a concentration gradient of the diffusible proteolytic enzyme). The existence of unique global mild solution is proved using the theory of fractional powers of analytic semigroup generators.