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 - <p style="text-align: justify;">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&nbsp; Perthame, Quirόs, and Vázquez [13].</p>