Existence of weak solutions to a Cahn–Hilliard–Biot system

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–Hillia...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 81; p. 104194
Main Authors Abels, Helmut, Garcke, Harald, Haselböck, Jonas
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2025
Subjects
Biot’s equations
Cahn–Hilliard equation
Existence analysis
Maximal regularity
Mixed boundary conditions
Poroelasticity
35K41
Mixed boundary conditions
Poroelasticity
35A01
Biot’s equations
35D30
Maximal regularity
74B10
Cahn–Hilliard equation
Existence analysis
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Summary: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.
ISSN:1468-1218
DOI:10.1016/j.nonrwa.2024.104194