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, Quirόs, and Vázquez [13].