Interfaces and Free Boundaries
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Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries
N.D. Alikakos (1), Paul C. Fife (2), G. Fusco (3) and C. Sourdis (4)
(1) Department of Mathematics, University of North Texas, 408 General Academic Building, P.O. Box 311430, TX 76203-1430, DENTON, UNITED STATES(2) Department of Mathematics, University of Utah, 155 South 1400 East, UT 84112-0090, SALT LAKE CITY, UNITED STATES
(3) Dipartimento di Matematica, Università degli Studi dell'Aquila, v. Vetoio, loc. Coppito, I-67100, L'AQUILA, ITALY
(4) Department of Mathematics, University of Athens, Panepistimioupolis, GR-157 84, ATHENS, GREECE
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 $\e$ 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 $\e$ is related to large anisotropy. The existence of such a heteroclinic, and its dependence on $\e$, is proved. In addition, its robustness is investigated by establishing its spectral stability.
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