On the Existence of Strong Solutions to the Cahn-Hilliard-Darcy system with mass source
Analysis of PDEs
2020-09-29 v1
Abstract
We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn-Hilliard-Darcy (CHD) type system with transport and mass source. A relevant physical application is related to tumor growth dynamics, which in particular justifies the occurrence of a mass inflow. We study the initial-boundary value problem for this model and prove global existence and uniqueness of strong solutions in two space dimensions as well as local existence in three space dimensions.
Keywords
Cite
@article{arxiv.2009.13344,
title = {On the Existence of Strong Solutions to the Cahn-Hilliard-Darcy system with mass source},
author = {Andrea Giorgini and Kei Fong Lam and Elisabetta Rocca and Giulio Schimperna},
journal= {arXiv preprint arXiv:2009.13344},
year = {2020}
}