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

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 conveys a singular perturbation. The motivation comes from a multi-order-parameter phase field model developed by Braun et al [5] and [22] for the description of crystalline interphase boundaries. In this, the smallness of is related to large anisotropy. The existence of such a heteroclinic, and its dependence on , 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