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Phase field models frequently provide insight to phase transitions, and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via…

Soft Condensed Matter · Physics 2015-09-30 Alpha A Lee , Andreas Münch , Endre Süli

We discuss two doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results…

Numerical Analysis · Mathematics 2020-12-17 Marco Salvalaglio , Axel Voigt , Steven M. Wise

This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…

Analysis of PDEs · Mathematics 2020-07-09 Elie Bretin , Simon Masnou , Arnaud Sengers , Garry Terii

We extend the doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion, which yield more accurate approximations than classical degenerate Cahn-Hilliard (DCH) models, to the anisotropic case. We consider both weak and…

Numerical Analysis · Mathematics 2020-12-17 Marco Salvalaglio , Maximilian Selch , Axel Voigt , Steven M. Wise

This paper presents an existence result for the anisotropic Cahn--Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account an anisotropic energy. The model allows for the degeneracy of…

Analysis of PDEs · Mathematics 2025-02-20 Harald Garcke , Patrik Knopf , Andrea Signori

We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…

Analysis of PDEs · Mathematics 2025-10-10 Monica Conti , Stefania Gatti , Andrea Giorgini , Giulio Schimperna

The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…

Analysis of PDEs · Mathematics 2020-07-03 Virginie Ehrlacher , Greta Marino , Jan-Frederik Pietschmann

We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric singular kernel. We define a notion of weak solution adapted to…

Analysis of PDEs · Mathematics 2026-05-22 Elisa Davoli , Greta Marino , Jan-Frederik Pietschmann

We propose in this paper a new multiphase Cahn-Hilliard model with doubly degenerate mobilities. We prove by a formal asymptotic analysis that it approximates with second order accuracy the multiphase surface diffusion flow with mobility…

Numerical Analysis · Mathematics 2023-04-19 Elie Bretin , Roland Denis , Simon Masnou , Arnaud Sengers , Garry Terii

We consider the existence of suitable weak solutions to the Cahn-Hilliard equation with a non-constant (degenerate) mobility on a class of evolving surfaces. We also show weak-strong uniqueness for the case of a positive mobility function,…

Analysis of PDEs · Mathematics 2025-08-04 Charles M. Elliott , Thomas Sales

We study a bulk-surface Cahn--Hilliard model with non-degenerate mobility and singular potentials in two dimensions. Following the ideas of the recent work by Conti, Galimberti, Gatti, and Giorgini [Calc. Var. Partial Differential…

Analysis of PDEs · Mathematics 2026-03-05 Jonas Stange

The Functionalized Cahn-Hilliard equation has been proposed as a model for the interfacial energy of phase-separated mixtures of amphiphilic molecules. We study the existence of a nonnegative weak solutions of a gradient flow of the…

Analysis of PDEs · Mathematics 2023-10-09 Shibin Dai , Qiang Liu , Toai Luong , Keith Promislow

In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving…

Mathematical Physics · Physics 2015-07-10 Alpha Albert Lee , Andreas Münch , Endre Süli

The Cahn-Hilliard equation is a widely used model for describing phase separation processes in a binary mixture. In this paper, we investigate the viscous Cahn-Hilliard equation with a degenerate, phase-dependent mobility. We define the…

Analysis of PDEs · Mathematics 2024-09-04 Toai Luong

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

We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…

Analysis of PDEs · Mathematics 2022-01-19 Helmut Abels , Yutaka Terasawa

The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…

Analysis of PDEs · Mathematics 2023-07-20 Christoph Helmer , Ansgar Jüngel

We consider a general class of bulk-surface convective Cahn--Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn--Hilliard type allow for dynamic…

Analysis of PDEs · Mathematics 2024-07-23 Patrik Knopf , Jonas Stange

The Cahn-Hilliard equation is a fundamental model for phase separation phenomena. Its rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link interacting particle systems and continuous descriptions, has…

Analysis of PDEs · Mathematics 2024-07-08 Charles Elbar , Jakub Skrzeczkowski

In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…

Analysis of PDEs · Mathematics 2016-09-16 Christian Heinemann , Christiane Kraus
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