Abels, Helmut and Garcke, Harald and Haselboeck, Jonas (2025) Existence of weak solutions to a Cahn-Hilliard-Biot system. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 81: 104194. ISSN 1468-1218, 1878-5719
Full text not available from this repository. (Request a copy)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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PHASE-SEPARATION; DARCY SYSTEM; DIFFUSION; MODEL; STRESS; Cahn-Hilliard equation; Biot's equations; Poroelasticity; Existence analysis; Mixed boundary conditions; Maximal regularity |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Mar 2026 09:11 |
| Last Modified: | 03 Mar 2026 09:11 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63496 |
Actions (login required)
 |
View Item |
