TY - JOUR T1 - Diffusion with a Discontinuous Potential: A Non-Linear Semigroup Approach AU - Kim , Yong-Jung AU - Slemrod , Marshall JO - Analysis in Theory and Applications VL - 2 SP - 178 EP - 190 PY - 2021 DA - 2021/04 SN - 37 DO - http://doi.org/10.4208/ata.2021.pr80.01 UR - https://global-sci.org/intro/article_detail/ata/18770.html KW - Nonlinear semigroups, tumor growth models, Hele-Shaw diffusion. AB -

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].