MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R2
Pino_Manuel_del_Multiple.pdf (467.8Kb)Abstract
We construct a new class of entire solutions for the Allen-Cahn equation
u + (1 u2)u = 0, in R2( C). Given k 1, we nd 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 0 < 1 < : : : <
2k = 0+2 such that limr!+1 u(rei ) = (1)j uniformly in on compact subsets
of ( j ; j+1), for j = 0; : : : ; 2k 1.
Patrocinador
This work has been partly supported by chilean research
grants Fondecyt 1070389, 1050311, 1090103, FONDAP, an ECOS-CONICYT contract
C05E05 and an Earmarked Grant from RGC of Hong Kong and Focused Research
Scheme of CUHK of Hong Kong. The third author was particaly supported by the
ANR-08-BLAN-0335-01.
Identifier
URI: https://repositorio.uchile.cl/handle/2250/125431
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