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Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it is known that solutions computed using the HDG scheme…

Numerical Analysis · Mathematics 2026-01-05 Jiannan Jiang , Noel J. Walkington , Yukun Yue

Globular proteins as well as recently synthesized colloids engineered with differently charged surface regions have in common a reduced bonding valence and a complex interaction pattern dominated by like-charge attraction and…

Soft Condensed Matter · Physics 2024-02-02 Daniele Notarmuzi , Emanuela Bianchi

This paper addresses the asymptotic development of order 2 by Gamma convergence of the Cahn-Hillard functional with Dirichlet boundary conditions, where the potential has subquadratic growth near the wells.

Analysis of PDEs · Mathematics 2025-10-20 Francesco Colasanto , Pascal Steinke

The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical…

Differential Geometry · Mathematics 2007-05-23 Viktor L. Ginzburg , Basak Z. Gurel

In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), 437-478 -- see also arXiv:1804.11290), the same authors have studied viscous…

Analysis of PDEs · Mathematics 2020-07-10 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper we analyze a fully discrete scheme for a general Cahn-Hilliard equation coupled with a nonsteady Magneto-hydrodynamics flow, which describes two immiscible, incompressible and electrically conducting fluids with different…

Numerical Analysis · Mathematics 2022-02-04 Hailong Qiu

We consider the classical initial and boundary value problem for the Cahn--Hilliard equation with non-degenerate mobility and singular (e.g., logarithmic) potential. We prove that any weak solution converges to a single equilibrium using…

Analysis of PDEs · Mathematics 2026-02-06 Maurizio Grasselli , Andrea Poiatti

We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full pressure. In dimension 2, this proves uniqueness for scalar…

Dynamical Systems · Mathematics 2018-08-30 Keith Burns , Vaughn Climenhaga , Todd Fisher , Daniel J. Thompson

In this article, the Hodge decomposition for any degree of differential forms is investigated on the whole space $\mathbb{R}^n$ and the half-space $\mathbb{R}^n_+$ on different scale of function spaces namely homogeneous and inhomogeneous…

Analysis of PDEs · Mathematics 2023-03-08 Anatole Gaudin

We revisit the existence problem of heteroclinic connections in $\mathbb{R}^N$ associated with Hamiltonian systems involving potentials $W:\mathbb{R}^N\to \mathbb{R}$ having several global minima. Under very mild assumptions on $W$ we…

Analysis of PDEs · Mathematics 2019-01-23 Andres Zuniga , Peter Sternberg

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 paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion type dynamics is derived on the basis…

Materials Science · Physics 2016-02-03 Gyula I. Toth , Mojdeh Zarifi , Bjorn Kvamme

We address the minimization of the Canham-Helfrich functional in presence of multiple phases. The problem is inspired by the modelization of heterogeneous biological membranes, which may feature variable bending rigidities and spontaneous…

Analysis of PDEs · Mathematics 2020-03-06 Katharina Brazda , Luca Lussardi , Ulisse Stefanelli

The Cahn-Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, often incur substantial computational cost,…

Numerical Analysis · Mathematics 2026-05-26 Yi Liu , Shuting Gu

The Cahn-Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss…

Fluid Dynamics · Physics 2017-10-26 Lennon O Naraigh , Jean-Luc Thiffeault

The present work demonstrates a robust protocol for probing localized electronic structure in condensed-phase systems, operating in terms of a recently proposed theory for decomposing the results of Kohn-Sham density functional theory in a…

Chemical Physics · Physics 2021-06-29 Janus J. Eriksen

In this paper we prove the convergence of a nonlocal version of the Cahn-Hilliard equation to its local counterpart as the nonlocal convolution kernel is scaled using suitable approximations of a Dirac delta in a periodic boundary…

Analysis of PDEs · Mathematics 2020-01-07 Stefano Melchionna , Helene Ranetbauer , Luca Scarpa , Lara Trussardi

We prove well-posedness and regularity for the stochastic pure Cahn-Hilliard equation under homogeneous Neumann boundary conditions, with both additive and multiplicative Wiener noise. In contrast with great part of the literature, the…

Analysis of PDEs · Mathematics 2018-10-03 Luca Scarpa

We consider a general energy functional for phase coexistence models, which comprises the case of Banach norms in the gradient term plus a double-well potential. We establish density estimates for $Q$-minima. Namely, the state parameters…

Analysis of PDEs · Mathematics 2017-09-27 Serena Dipierro , Alberto Farina , Enrico Valdinoci

In this paper we study optimal control problem for non local Cahn-Hilliard-Brinkman system which models phase separation of binary fluids in porous media. We consider the system in two dimensional bounded domain with regular potential. We…

Analysis of PDEs · Mathematics 2019-11-11 Sheetal Dharmatti , Mahendranath PL N