Slowly-Migrating Transition Layers for the Discrete Allen-Cahn and Cahn-Hilliard Equations

Files
94-163.pdf (288.36 KB)
Author(s)
Grant, Christopher P.
Van Vleck, Erik S.
Advisor(s)
Editor(s)
Associated Organization(s)
Organizational Unit
Organizational Unit
Series
Collections
Research Publications
Supplementary to:
Permanent Link
http://hdl.handle.net/1853/29552
Abstract
It has recently been proposed that spatially discretized versions of the Allen-Cahn and Cahn-Hilliard equations for modeling phase transitions have certain theoretical and phenomenological advantages over their continuous counterparts. This paper deals with one-dimensional discretizations and examines the extent to which dynamical metastability, which manifests itself in the original partial differential equations in the form of solutions with slowly-moving transition layers, is also present for the discrete equations. It is shown that, in fact, there are transition layer solutions that evolve at a speed bounded by [equation omitted], where 1/n is the spatial mesh size and ε is the interaction length.
Sponsor
Date
1994
Extent
Resource Type
Text
Resource Subtype
Pre-print
Rights Statement
Rights URI