Related papers: Low regularity potentials in heterogeneous Cahn--H…
In this paper we study a non-local Cahn-Hilliard equation with singular single-well potential and degenerate mobility. This results as a particular case of a more general model derived for a binary, saturated, closed and incompressible…
The phase separation between two immiscible liquids advected by a bidimensional velocity field is investigated numerically by solving the corresponding Cahn-Hilliard equation. We study how the spinodal decomposition process depends on the…
In Lagrangian coordinates, the local well-posedness of low regularity solutions is established for an ideal incompressible magnetohydrodynamic (MHD) system subject to a homogeneous background magnetic field. First, the MHD system is…
We propose a new Cahn-Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive…
We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn-Hilliard-type equation for two-phase flows and the Peterlin-Navier-Stokes equations for…
Well-posedness is proved for the stochastic viscous Cahn-Hilliard equation with homogeneous Neumann boundary conditions and Wiener multiplicative noise. The double-well potential is allowed to have any growth at infinity (in particular,…
We prove that the geodesic flow on a compact locally CAT(-1) space has the weak specification property, and give various applications. We show that every H\"older potential on the space of geodesics has a unique equilibrium state. We…
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…
We consider an energy functional combining the square of the local oscillation of a one--dimensional function with a double well potential. We establish the existence of minimal heteroclinic solutions connecting the two wells of the…
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…
We consider the nonlocal Cahn-Hilliard equation with singular (logarithmic) potential and constant mobility in three-dimensional bounded domains and we establish the validity of the instantaneous strict separation property. This means that…
The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution kernel. While this formulation admits a rich existence and…
We propose a simple nonlocal energy functional that is suitable for the continuum field characterization of nonperiodic and localized textures. The phenomenological functional is based on the pairwise direction-dependent interaction of…
The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental…
The global-in-time existence of weak solutions to a degenerate Cahn-Hilliard cross-diffusion system with singular potential in a bounded domain with no-flux boundary conditions is proved. The model consists of two coupled parabolic…
The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…
Consider a compact surface of genus $\geq 2$ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $2\pi$. Following the technique in the work of Burns, Climenhaga, Fisher, and Thompson,…
We refine the asymptotic estimates for minimizers of a class of nonlocal energy functionals of the form \[ \frac{1}{4} \iint_{\R^{2n} \setminus (\R^n \setminus \Omega)^2} \snr{u(x) - u(y)}^2 K(x - y) \,dx\,dy + \int_\Omega W(u(x)) \,dx, \]…
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…
A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are…