An integrodifferential model for phase transitions: Stationary solutions in higher space dimensions

Authors
Bates, PW Chmaj, A
Citation
Pw. Bates et A. Chmaj, An integrodifferential model for phase transitions: Stationary solutions in higher space dimensions, J STAT PHYS, 95(5-6), 1999, pp. 1119-1139
Citations number
33
Categorie Soggetti
Physics
Journal title
JOURNAL OF STATISTICAL PHYSICS
ISSN journal
00224715 → ACNP
Volume
95
Issue
5-6
Year of publication
1999
Pages
1119 - 1139
Database
ISI
SICI code
0022-4715(199906)95:5-6<1119:AIMFPT>2.0.ZU;2-F
Abstract
We study the existence and stability of stationary solutions of an integrod ifferential model for phase transitions, which is a gradient flow for a fre e energy functional with general nonlocal integrals penalizing spatial nonu niformity. As such, this model is a nonlocal extension of the Allen-Cahn eq uation, which incorporates long-range interactions. We find that the set of stationary solutions for this model is much larger than that of the Allen- Cahn equation.