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math.AP2025
Existence and Nonlocal-to-Local Convergence for Singular, Anisotropic Nonlocal Cahn-Hilliard Equations
Helmut Abels, Yutaka Terasawa
We study the nonlocal-to-local convergence for a nonlocal Cahn-Hilliard equation with anisotropic and singular kernels. In particular, we show convergence of weak solutions of the…
math.AP2025
Well-posedness and sharp interface limit of a non-isothermal Navier--Stokes/Allen--Cahn model
Helmut Abels, Alice Marveggio, Andrea Poiatti
We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove…
math.AP2025
Local Well-Posedness of the Cahn-Hilliard-Biot System
Helmut Abels, Jonas Haselböck
We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly c…