This article is available for purchase or by subscription. See below.
Abstract
|
We analytically and numerically study a fourth-order PDE modeling rough crystal
surface diffusion on the macroscopic level. We discuss existence of solutions globally
in time and long-time dynamics for the PDE model. The PDE, originally derived by
Katsevich is the continuum limit of a microscopic model of the surface dynamics,
given by a Markov jump process with Metropolis-type transition rates. We outline
the convergence argument, which depends on a simplifying assumption on the local
equilibrium measure that is valid in the high-temperature regime. We provide
numerical evidence for the convergence of the microscopic model to the PDE in this
regime.
|
PDF Access Denied
We have not been able to recognize your IP address
18.188.40.207
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
crystal surface relaxation, gradient flows, metropolis
rates
|
Mathematical Subject Classification 2010
Primary: 35Q70, 82D25
|
Milestones
Received: 16 March 2020
Revised: 19 November 2020
Accepted: 29 April 2021
Published: 12 February 2022
|
|