A discrete convolution model for phase transitions

Authors
Bates, PW Chmaj, A
Citation
Pw. Bates et A. Chmaj, A discrete convolution model for phase transitions, ARCH R MECH, 150(4), 1999, pp. 281-305
Citations number
23
Categorie Soggetti
Mathematics,"Mechanical Engineering
Journal title
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN journal
00039527 → ACNP
Volume
150
Issue
4
Year of publication
1999
Pages
281 - 305
Database
ISI
SICI code
0003-9527(1999)150:4<281:ADCMFP>2.0.ZU;2-1
Abstract
We study a discrete convolution model for Ising-like phase transitions. Thi s nonlocal model is derived as an l(2)-gradient flow for a Helmholtz free e nergy functional with general long range interactions. We construct traveli ng waves and stationary solutions, and study their uniqueness and stability . In particular, we find some criteria for "propagation" and "pinning", and compare our results with those for a previously studied continuum convolut ion model.