Maria G. Westdickenberg

A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit

Nous etudions un systeme sur reseau a variable de spin continue. Dans la premiere partie, nous etablissons deux resultats abstraits: des conditions suttisantes pour une inegalite de Sobolev logarithmique avec constante independante de la dimension (Theoreme 3), et des conditions suffisantes pour la convergence vers la limite hydrodynamique (Theoreme 8). Dans la seconde partie, nous utilisons ces resultats abstraits pour traiter un exemple specifique, a savoir la dynamique de Kawasaki avec un potentiel de type Ginzburg―Landau.

Relaxation to Equilibrium in the One-Dimensional Cahn--Hilliard Equation

We study the stability of a so-called kink profile for the one-dimensional Cahn--Hilliard problem on the real line. We derive optimal bounds on the decay to equilibrium under the assumption that the initial energy is less than three times the energy of a kink and that the initial

Energy barrier and \Gamma -convergence in the d-dimensional Cahn–Hilliard equation

\dot{H}^{-1}

Rare Events in Stochastic Partial Differential Equations on Large Spatial Domains

distance to a kink is bounded. Working with the

Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size

\dot{H}^{-1}

Higher multiplicity in the one-dimensional Allen-Cahn action functional

distance is natural, since the equation is a gradient flow with respect to this metric. Indeed, our method is to establish and exploit elementary algebraic and differential relationships among three natural quantities: the energy, the dissipation, and the

Metastability of the Cahn-Hilliard equation in one space dimension

\dot{H}^{-1}

Stochastics meets applied analysis : stochastic Ginzburg-Landau vortices and stochastic Landau-Lifshitz-Gilbert equation

distance to a kink. Along the way it is necessary and possible to control the time-dependent shift of the center of the

Optimal

L^2

L^1

closest kink. Our result is different from earlier results because we do not assume smallness of the initial distance to a kink; we assume only boundedness.