JournalsifbVol. 8 , No. 2DOI 10.4171/ifb/139

Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries

  • Paul C. Fife

    University of Utah, Salt Lake City, USA
  • C. Sourdis

    University of Athens, Greece
  • Nicholas D. Alikakos

    University of Athens, Greece
  • Giorgio Fusco

    Università degli Studi dell'Aquila, Italy
Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries cover

Abstract

Mathematically, the problem considered here is that of heteroclinic connections for a system of two second order differential equations of Hamiltonian type, in which a small parameter \e\e conveys a singular perturbation. The motivation comes from a multi-order-parameter phase field model developed by Braun et al \cite{BCMcFW} and \cite{T} for the description of crystalline interphase boundaries. In this, the smallness of \e\e is related to large anisotropy. The existence of such a heteroclinic, and its dependence on \e\e, is proved. In addition, its robustness is investigated by establishing its spectral stability.