JournalsifbVol. 8, No. 2pp. 159–183

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
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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.

Cite this article

Paul C. Fife, C. Sourdis, Nicholas D. Alikakos, Giorgio Fusco, Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries. Interfaces Free Bound. 8 (2006), no. 2, pp. 159–183

DOI 10.4171/IFB/139