Bistable Boundary Reactions in Two Dimensions

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Abstract

In a bounded domain Ω ⊂ ℝ2 with smooth boundary we consider the problem where ν is the unit normal exterior vector, ε > 0 is a small parameter and f is a bistable nonlinearity such as f(u) = sin(πu) or f(u) = (1 - u2)u. We construct solutions that develop multiple transitions from -1 to 1 and vice-versa along a connected component of the boundary ∂Ω. We also construct an explicit solution when Ω is a disk and f(u) = sin(πu).

Original languageEnglish
Pages (from-to)89-140
Number of pages52
JournalArchive for Rational Mechanics and Analysis
Volume200
Issue number1
DOIs
Publication statusPublished - 1 Apr 2011

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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