This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

This paper reviews the derivation of some macroscopic models for superconductivity and
also some of the mathematical challenges posed by these models. The paper begins by …

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 …

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 …

In this paper we consider the Cahn-Hilliard mathematical continuum model of spinodal
decomposition (or phase separation) of a binary alloy. The phenomenological model is …

..." What do you call work?"" Why ain't that work?" Tom resumed his whitewashing, and
answered carelessly:" Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom …

Recent theoretical advances in the mathematical treatment of geometric interface motion
make more tractable the theory of a wide variety of materials science problems where the …

We study properties of the solutions of a family of second-order integrodifferential equations,
which describe the large scale dynamics of a class of microscopic phase segregation …

We study the backward Euler method with variable time steps for abstract evolution
equations in Hilbert spaces. Exploiting convexity of the underlying potential or the angle …

Consider the phase-field system of equations aaQt-EAQ+ E-'f (4)= au,(1.1) cut-Au=-Qt(1.2)
where f is the derivative of a smooth double equal well potential, a, u, and c are positive …