Nucleation in the one-dimensional Cahn-Hilliard Model
type: CreativeWork
description: In the first part we study the one-dimensional Cahn-Hilliard equation. The dynamics can be reduced to an inertial manifold. Using Conley index theory we study the fine structure of the global attractor. In particular we consider the basin of attraction D of the homogenuous solution. We show that the first spikes always lie on the boundary of D and minimize the free Ginzburg-Landau energy on this boundary. In the second part we introduce an additional stochastic noise term in the equation. Now solutions leave the domain D almost surely. We prove that the exit points are located near the first spikes with overwhelming probabiltity if the noise intensity is small. To some extend this describes the physical phenomenon of 'nucleation'.
abstract: In the first part we study the one-dimensional Cahn-Hilliard equation. The dynamics can be reduced to an inertial manifold. Using Conley index theory we study the fine structure of the global attractor. In particular we consider the basin of attraction D of the homogenuous solution. We show that the first spikes always lie on the boundary of D and minimize the free Ginzburg-Landau energy on this boundary. In the second part we introduce an additional stochastic noise term in the equation. Now solutions leave the domain D almost surely. We prove that the exit points are located near the first spikes with overwhelming probabiltity if the noise intensity is small. To some extend this describes the physical phenomenon of 'nucleation'.
author: Gawron, Bernhard
language: eng
keywords: info:eu-repo/classification/ddc/510, Cahn-Hilliard-Gleichung, Große Abweichung, Attraktor, Inertialmannigfaltigkeit, Conley-Index, Mathematik, Cahn-Hilliard-Cook Gleichung, Stochastische Cahn-Hilliard Gleichung, Prinzip der grossen Abweichung, Austritt aus einem Gebiet, Cahn-Hilliard equation, attractor, inertial manifold, Cahn-Hilliard-Cook equation, exit problem
date published: 2006
date modified: 2026-07-30T19:42:56Z
provider: RWTH Aachen University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Publikationsserver der RWTH Aachen University