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

• Published in: Nonlinear analysis: real world applications Vol. 81; p. 104194
• Main Authors: Abels, Helmut, Garcke, Harald, Haselböck, Jonas
• Format: Journal Article
• Language: English
• 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

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...