ON THE STATIONARY CAHN-HILLIARD EQUATION - BUBBLE SOLUTIONS

Authors
WEI JC WINTER M
Citation
Jc. Wei et M. Winter, ON THE STATIONARY CAHN-HILLIARD EQUATION - BUBBLE SOLUTIONS, SIAM journal on mathematical analysis (Print), 29(6), 1998, pp. 1492-1518
Citations number
35
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on mathematical analysis (Print) → ACNP
ISSN journal
00361410
Volume
29
Issue
6
Year of publication
1998
Pages
1492 - 1518
Database
ISI
SICI code
0036-1410(1998)29:6<1492:OTSCE->2.0.ZU;2-E
Abstract
We study stationary solutions of the Cahn-Hilliard equation in a bound ed smooth domain that have an interior spherical interface (bubbles). We show that a large class of interior points (the ''nondegenerate pea k'' points) have the following property: there exists such a solution whose bubble center lies close to a given nondegenerate peak point. Ou r construction uses, among others, the Liapunov-Schmidt reduction meth od and exponential asymptotics.