Analysis of the Heteroclinic Connection in a Singularly Perturbed System Arising from the Study of Crystalline Grain Boundaries

Mathematically, the problem considered here is that of heteroclinic connections for a system of two second order differential equations of gradient type, in which a small parameter ǫ conveys a singular perturbation. The motivation comes from a multi-order-parameter phase field model developed by Braun et al [5] and [23] for the description of crystalline interphase boundaries. In this, the smallness of ǫ is related to large anisotropy. The existence of such a heteroclinic, and its dependence on ǫ, is proved. In addition, its stability is established within the context of the associated evolutionary phase field equations.