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arXiv · 2403.07515

Existence of Weak Solutions to a Cahn-Hilliard-Biot System

Helmut Abels·Harald Garcke·Jonas Haselböck
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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.

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Helmut Abels, Harald Garcke, Jonas Haselböck. 2024-03-12. Existence of Weak Solutions to a Cahn-Hilliard-Biot System. https://doi.org/10.1016/j.nonrwa.2024.104194

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