10 papers
Higher Order Convergence for the Sharp Interface Limit of 3D Navier--Stokes/Allen--Cahn Systems
Helmut Abels, Mingwen Fei, Yadong Liu +1
We show convergence of solutions to a Navier--Stokes/Allen--Cahn system as the interfacial thickness tends to zero for well-prepared initial data as long as the lim…
Local Well-Posedness of a Model for Stress-Driven Growth in the Presence of Nutrients
Helmut Abels, Julian Blawid, Georg Dolzmann
A model for morphoelastic growth, that is, growth influenced by elastic stress, driven by the absorption of nutrients is considered. The model features a multiplicative decompositi…
Sharp Interface Limit for a Mass-Conserving Navier-Stokes/Allen-Cahn System with Different Viscosities
Helmut Abels, Hanifah Mumtaz
We perform a rigorous examination of the sharp interface limit of a coupled Navier-Stokes and mass-conserving Allen-Cahn system in a two-dimensional, bounded, and smooth domain as…
Nonlocal-to-local -convergence of convolution operators with singular, anisotropic kernels
Helmut Abels, Christoph Hurm, Patrik Knopf
We study nonlocal convolution-type operators with singular, possibly anisotropic kernels. Our main objective is to establish and quantify their nonlocal-to-local convergence to a l…
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…
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…
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…
Convergence of the Nonlocal Allen-Cahn Equation to Mean Curvature Flow
Helmut Abels, Christoph Hurm, Maximilian Moser
We prove convergence of the nonlocal Allen-Cahn equation to mean curvature flow in the sharp interface limit, in the situation when the parameter corresponding to the kernel goes t…
Convergence of a Convective Allen-Cahn Equation to a Transport Equation
Helmut Abels
We show convergence of solutions of a convective Allen-Cahn equation for a given smooth and divergence free velocity field to a transport equation for an evolving interface in the…
Maximal -regularity for -dependent fractional heat equations with Dirichlet conditions
Helmut Abels, Gerd Grubb
We prove optimal regularity results in -based function spaces in space and time for a large class of linear parabolic equations with a nonlocal elliptic operator in bounded do…