An overview will be given of some nonlinear parabolic-like evolution problems which are off
the classical beaten track, but have increased in importance during the past decade. The …

This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

Hysteresis is an exciting and mathematically challenging phenomenon that oc curs in rather
different situations: jt, can be a byproduct offundamental physical mechanisms (such as …

Publisher Summary This chapter focuses on the Cahn–Hilliard equation. In the context of the
Cahn–Hilliard equation, the two components could refer, for example, to a system with two …

We prove that level surfaces of solutions to the Cahn-Hilliard equation tend to solutions of
the Hele-Shaw problem under the assumption that classical solutions of the latter exist. The …

A nonlocal reaction-diffusion equation is presented and analysed using matched asymptotic
expansions and multiple timescales. The problem models a binary mixture undergoing …

We show by using formal asymptotics that the zero level set of the solution to the Cahn–
Hilliard equation with a concentration dependent mobility approximates to lowest order in ɛ …

Entropy inequalities, correlation functions, couplings between stochastic processes are
powerful techniques which have been extensively used to give arigorous foundation to the …

In this paper we study the coupling of the Navier–Stokes equations and the Cahn–Hilliard
equation which stands for a model of a multi‐phase fluid under shear. We first study …

We review physical, mathematical, and numerical derivations of the binary Cahn–Hilliard
equation (after John W. Cahn and John E. Hilliard). The phase separation is described by …