Boundary-clustered interfaces for the Allen-Cahn equation

Andrea Malchiodi, Wei Ming Ni, Juncheng Wei

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16 Scopus citations

Abstract

We consider the Allen-Cahn equation where Ω = B1(0) is the unit ball in ℝn and ε > 0 is a small parameter. We prove the existence SN of a radial solution uε having N interfaces {uε(r)=0} = {n-ary union}Nj=1, where 1> rε1 > rε2 >...> rεN are such that 1-rε1 ~ε log(1/ε) and rεj-1 - rεj ~ ε log(1/ε) for j = 2,..., N. Moreover, the Morse index of uε in H1rε) is exactly N.

Original languageEnglish (US)
Pages (from-to)447-468
Number of pages22
JournalPacific Journal of Mathematics
Volume229
Issue number2
DOIs
StatePublished - Feb 2007

Keywords

  • Allen-Cahn equation
  • Boundary clustered interfaces

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