Contact angle selection for interfaces in growing domains

Rafael Monteiro, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study interfaces in an Allen-Cahn equation, separating two metastable states. Our focus is on a directional quenching scenario, where a parameter renders the system bistable in a half plane and monostable in its complement, with the region of bistability expanding at a fixed speed. We show that the growth mechanism selects a contact angle between the boundary of the region of bistability and the interface separating the two metastable states. Technically, we focus on a perturbative setting in a vicinity of a symmetric situation with perpendicular contact. The main difficulty stems from the lack of Fredholm properties for the linearization in translation invariant norms. We overcome those difficulties establishing Fredholm properties in weighted spaces and farfield-core decompositions to compensate for negative Fredholm indices.

Original languageEnglish (US)
Pages (from-to)1086-1102
Number of pages17
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume98
Issue number7
DOIs
StatePublished - Jul 2018

Keywords

  • Allen-Cahn equation
  • contact
  • directional quenching
  • phase separation angle

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