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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 couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2026-05-01 Helmut Abels , Jonas Haselböck

In this paper, we study the sharp interface limit for solutions of the Cahn-Hilliard equation with disparate mobilities. This means that the mobility function degenerates in one of the two energetically favorable configurations, suppressing…

Analysis of PDEs · Mathematics 2022-01-19 Milan Kroemer , Tim Laux

A nonlocal Cahn-Hilliard model with a nonsmooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg-Landau energy…

Analysis of PDEs · Mathematics 2021-09-13 Olena Burkovska , Max Gunzburger

We consider a diffuse interface model that describes the macro- and micro-phase separation processes of a polymer mixture. The resulting system consists of a Cahn-Hilliard equation and a Cahn-Hilliard-Oono type equation endowed with the…

Analysis of PDEs · Mathematics 2024-05-01 Bohan Ouyang

We consider a Cahn-Hilliard equation which is the conserved gradient flow of a nonlocal total free energy functional. This functional is characterized by a Helmholtz free energy density, which can be of logarithmic type. Moreover, the…

Analysis of PDEs · Mathematics 2013-11-15 Helmut Abels , Stefano Bosia , Maurizio Grasselli

We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimeter, and we discuss the possible Wulff shapes obtainable in…

Metric Geometry · Mathematics 2021-07-20 Giacomo Del Nin , Mircea Petrache

An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…

Analysis of PDEs · Mathematics 2021-06-03 Pierluigi Colli , Takeshi Fukao , Luca Scarpa

We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space $\mathbb{H}^{n+1}$ with contact angle $\theta \in (0,\pi)$ and dimension $n \geq 2$. As a consequence, we obtain the generalized…

Differential Geometry · Mathematics 2026-05-21 Gaoming Wang , Xuwen Zhang

We present a finite-volume based numerical scheme for a nonlocal Cahn-Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn-Hilliard equations. The equation of interest is a…

Numerical Analysis · Mathematics 2024-04-08 Rainey Lyons , Grigor Nika , Adrian Muntean

The Cahn-Hilliard energy landscape on the torus is explored in the critical regime of large system size and mean value close to $-1$. Existence and properties of a "droplet-shaped" local energy minimizer are established. A standard mountain…

Analysis of PDEs · Mathematics 2016-03-17 Michael Gelantalis , Alfred Wagner , Maria G. Westdickenberg

We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…

Analysis of PDEs · Mathematics 2024-08-15 Helmut Abels , Harald Garcke , Andrea Poiatti

The short-time stability of concentration profiles in coherent periodic multilayers consisting of two components with large miscibility gap is investigated by analysing stationary solutions of the Cahn-Hilliard diffusion equation. The…

Materials Science · Physics 2009-10-31 Martina Hentschel , Manfred Bobeth , Gerhard Diener , Wolfgang Pompe

We consider a class of nonlocal Cahn-Hilliard equations in a bounded domain $\Omega\subset\mathbb{R}^{d}$ $(d\in\{2,3\})$, subject to a nonlocal kinetic rate dependent dynamic boundary condition. This diffuse interface model describes phase…

Analysis of PDEs · Mathematics 2024-12-11 Maoyin Lv , Hao Wu

We construct gradient structures for free boundary problems with nonlinear elasticity and study the impact of moving contact lines. In this context, we numerically analyze how phase-field models converge to certain sharp-interface limits…

Analysis of PDEs · Mathematics 2024-06-26 Leonie Schmeller , Dirk Peschka

We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold…

Differential Geometry · Mathematics 2019-07-01 Otis Chodosh , Daniel Ketover , Davi Maximo

We investigate a new phase field model for representing non-oriented interfaces, approximating their area and simulating their area-minimizing flow. Our contribution is related to the approach proposed in arXiv:2105.09627 that involves ad…

Optimization and Control · Mathematics 2025-07-03 Elie Bretin , Antonin Chambolle , Simon Masnou

This paper is concerned with a diffuse interface model called as Navier-Stokes/Cahn-Hilliard system. This model is usually used to describe the motion of immiscible two-phase flow with diffusion interface. For the periodic boundary value…

Analysis of PDEs · Mathematics 2021-09-06 Yazhou Chen , Hakho Hong , Xiaoding Shi

A unified energy principle approach is presented for analysing the magnetohydrodynamic (MHD) stability of plasmas consisting of multiple ideal and relaxed regions. By choosing an appropriate gauge, we show that the plasma displacement…

Plasma Physics · Physics 2015-05-13 R. L. Mills , M. J. Hole , R. L. Dewar

Hyperuniform structures are disordered, correlated systems in which density fluctuations are suppressed at large scales. Such a property generalizes the concept of order in patterns and is relevant across diverse physical systems. We…

Soft Condensed Matter · Physics 2025-09-09 Abel H. G. Milor , Otto Sumray , Heather A. Harrington , Axel Voigt , Marco Salvalaglio

A common paradigm in phase-field models with singular potentials is that global-in-time weak solutions converge to a single equilibrium only after undergoing asymptotic regularization. However, in arXiv:2510.17296 we introduced a novel…

Analysis of PDEs · Mathematics 2026-04-01 Maurizio Grasselli , Andrea Poiatti