English

On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms

Analysis of PDEs 2018-03-26 v2 Tissues and Organs

Abstract

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn--Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered for the pressure variable, which allows for the source terms to be dependent on the solution variables.

Keywords

Cite

@article{arxiv.1611.00234,
  title  = {On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms},
  author = {Harald Garcke and Kei Fong Lam},
  journal= {arXiv preprint arXiv:1611.00234},
  year   = {2018}
}

Comments

18 pages, changed proof from fixed point argument to Galerkin approximation

R2 v1 2026-06-22T16:38:42.727Z