Multiple-end solutions to the Allen-Cahn equation in R-2
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AbstractWe construct a new class of entire solutions for the Allen-Cahn equation Delta u + (1 - u(2))u = 0, in R-2(similar to C). Given k >= 1, we find a family of solutions whose zero level sets are, away from a compact set, asymptotic to 2k straight lines (which we call the ends). These solutions have the property that there exist theta(0) < theta(1) < ... < theta(2k) = theta(0) + 2 pi such that lim(r ->+infinity) u(r e(i theta)) = (-1)(j) uniformly in theta on compact subsets of (theta(j), theta(j+1)), for j = 0, ... , 2k - 1. (C) 2009 Published by Elsevier Inc.
All Author(s) Listdel Pino M, Kowalczyk M, Pacard F, Wei JC
Journal nameJournal of Functional Analysis
Detailed descriptionTo ORKTS:

Year2010
Month1
Day15
Volume Number258
Issue Number2
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Pages458 - 503
ISSN0022-1236
eISSN1096-0783
LanguagesEnglish-United Kingdom
KeywordsAllen-Cahn equation; Infinite-dimensional Lyapunov-Schmidt reduction; Moduli spaces; Multiple-end solutions; Toda system
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2020-23-10 at 01:35