The aim of this paper is to study the well-posedness and long time behavior, in terms of finite-dimensional attractors, of a perturbed Cahn–Hilliard equation. This equation differs from the usual Cahn–Hilliard by the presence of the term ε(−Δu+ f (u)). In particular, we prove the existence of a robust family of exponential attractors as ε goes to zero.

Abstract. We develop a new infinite dimensional gluing method for fractional elliptic equations. In Part I, as a model problem, we construct a solution of the fractional Allen–Cahn equation vanishing on a rotationally symmetric surface which resembles a catenoid and has sub-linear growth at infinity. In Part II, we construct counterexamples to De Giorgi Conjectures to fractional Allen-Cahn equa...

LEPTO event generator is modified to describe the azimuthal modulations arising from Cahn and Sivers effects. The comparisons with some existing data in the current fragmentation region of SIDIS are presented. The predictions for Cahn and Sivers asymmetries in the target fragmentation region are presented for SIDIS of 12 GeV electrons off proton target.

Abstract. We consider the nucleation of one-dimensional stochastic Cahn-Hilliard dynamics with the standard double well potential. We design the string method for computing the most probable transition path in the zero temperature limit based on large deviation theory. We derive the nucleation rate formula for the stochastic Cahn-Hilliard dynamics through finite dimensional discretization. We a...

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn–Hilliard–Darcy system coupled with an elliptic reactiondiffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn–Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered ...

We show existence and uniqueness of a solution for the non-local vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and non-local constraints. Furthermore, we propose and analyze a primal-dual active set method for local and non-local vector-valued Allen-Cahn variational inequalities. Convergence of the primal-dual active set algorithm is s...

We introduce unconditionally stable finite element approximations for anisotropic Allen– Cahn and Cahn–Hilliard equations. These equations frequently feature in phase field models that appear in materials science. On introducing the novel fully practical finite element approximations we prove their stability and demonstrate their applicability with some numerical results. We dedicate this artic...

This talk is about two-component Bose-Einstein condensate in a harmonic trap. The aim is to describe the shape and the spatial configuration of the ground state pairs. We will show links between our model and other mathematical problems : optimal partition problems and the Cahn-Hilliard model for phase transition. These links appear in our model in the limit when intercomponent particle interac...

Some known models in phase separation theory (Hele-Shaw, nonlocal mean curvature motion) and their approximated phase field models (Cahn–Hilliard, nonlocal Allen-Cahn) are used to generate planar curve evolution without shrinkage, with application to shape recovery. This turns out to be a level set approach to an area preserving geometric flow, in the spirit of Sapiro and Tannenbaum [36]. We di...