Existence of Heteroclinic Orbits for a Corner Layer Problem in Anisotropic Interfaces

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 conveys a singular perturbation. The physical motivation comes from a multi-order-parameter phase field model developed by Braun et al [BCMcFW] and [T] for the description of crystalline interphase boundaries. In this, the smallness of is related to large anisotropy. The mathematical interest stems from the fact that the smoothness and normal hyperbolicity of the critical manifold fails at certain points. Thus the well-developed geometric singular perturbation theory [Fe], [J] does not apply. The existence of such a heteroclinic, and its dependence on , is proved via a functional analytic approach.