Diffusion with a Discontinuous Potential: a Non-Linear Semigroup Approach

This paper studies existence of mild solution to a sharp cut off model for contact driven tumor growth.Analysis is based on application of the Crandall-Liggett theorem for ω-quasi-contractive semigroups on the Banach space L1 (Ω).Furthermore,numerical computations are provided which compare the sharp cut off model with the tumor growth model of Perthame,Quirós,and Vázquez13].