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

Abstract

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 omega-quasi-contractive semigroups on the Banach space L-1 (Omega). Furthermore, numerical computations are provided which compare the sharp cut off model with the tumor growth model of Perthame, Quiros, and Vazquez [13].