Diblock copolymers are a class of materials formed by the reaction of two linear polymers. The different structures taken on by these polymers grant them special properties, which can prove useful in applications such as the development of new adhesives and asphalt additives. We consider a model for the formation of diblock copolymers first proposed by Ohta and Kawasaki [26]. Their model yields...

In this paper, we consider nonlinear multidimensional Cahn–Hilliard and Kuramoto–Sivashinsky equations that have many important applications in physics chemistry, a certain natural generalization of these two to which refer as the generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation. For an arbitrary number spatial independent variables, present complete list cases when latter equation admit...

We are concerned with the Cahn–Hilliard/Navier–Stokes equations for stationary compressible flows in a three-dimensional bounded domain. The governing consist of Navier–Stokes describing fluid and Cahn–Hilliard-type diffuse equation mass concentration difference. prove existence weak solutions when adiabatic exponent $$\gamma $$ satisfies >\frac{4}{3}$$ . proof is based on weighted total energy...

We build a family of entire solutions to the Allen-Cahn equation in RN+1 for N ≥ 3, whose level set approaches the higher dimensional catenoid in a compact region and has two logarithmic ends governed by the solutions to the Liouville equation.

We analyze a semidiscrete scheme for the Cahn-Hilliard equation in one space dimension, when the interface length parameter is equal to zero. We prove convergence of the scheme for a suitable class of initial data, and we identify the limit equation. We also characterize the long-time behavior of the limit solutions. keywords: Nonconvex functionals, forward-backward parabolic equations, finite ...

We study an Allen–Cahn equation perturbed by a multiplicative stochastic noise that is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive a uniform bound for the diffuse surface area, prove the tightness of solutions in the sharp interface limit, and show the convergence to phase-indicator functions.

The grounding process relies on the evidence that speakers give about their understanding (Clark and Schaefer, 1989). However in existing models of grounding (Cahn, 1992; Cahn and Brennan, 1999; Traum, 1999) evidence of understanding is assumed to be symmetrically and synchronously shared by the speakers. We propose a grounding model based on (Cahn, 1992) that removes these simplifications; we ...

We carry out rigorous error analysis for some energy stable time discretization schemes developed in [20] for a Cahn-Hilliard phase-field model and in [19] for an Allen-Cahn phase-field model.