Existence of Weak Solutions to a Cahn-Hilliard-Biot System
Abstract
We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including phase-field dependent material properties, with the Cahn-Hilliard equation to model the evolution of the solid, and is further augmented by a visco-elastic regularization of Kelvin-Voigt type. To obtain this result, we approximate the problem in two steps, where first a semi-Galerkin ansatz is employed to show existence of weak solutions to regularized systems, for which later on compactness arguments allow limit passage. Notably, we also establish a maximal regularity theory for linear visco-elastic problems.
Keywords
Cite
@article{arxiv.2403.07515,
title = {Existence of Weak Solutions to a Cahn-Hilliard-Biot System},
author = {Helmut Abels and Harald Garcke and Jonas Haselböck},
journal= {arXiv preprint arXiv:2403.07515},
year = {2024}
}