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 …

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 …

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 …

GLOBAL ASYMPTOTIC LIMIT OF SOLUTIONS OF THE CAHN-HILLIARD EQUATION XINFU
CHEN Abstract 1. Introduction lkuE = l ί ^ = > (x Page 1 J. DIFFERENTIAL GEOMETRY Vol. 44 …

We study the asymptotic behavior of radially symmetric solutions of the nonlocal equation
ε\phi_t-ε Δ ϕ+ 1 ε W'(ϕ)-\lambda_ ε (t)= 0 in a bounded spherically symmetric domain …

We study the full-time dynamics of the initial value problem, for uε= uε (x, t), where 0< ε⪡ 1
and F (u) has global minimum 0 at u=±1. We assume that u0 (·) is bounded, continuous and …

In this paper we study the dynamics of the one-dimensional Cahn-Hilliard equation in a
neighborhood of an equilibrium having N+ 1 transition layers. An approximation for an N …

In this paper we present a conservative numerical method for the Cahn–Hilliard equation
with Dirichlet boundary conditions in complex domains. The method uses an unconditionally …

In a multidimensional domain, the slow motion behavior of internal layer solutions with
spherical interfaces, referred to as bubble solutions, is analyzed for the nonlocal Allen–Cahn …

Metastable patterns are those that change very slowly, to such an extent that they act like
stable equilibria for a long time, but are eventually destroyed. They, along with stable …