Advances in Differential Equations
- Adv. Differential Equations
- Volume 12, Number 6 (2007), 623-668.
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 $\epsilon$ conveys a singular perturbation. The physical motivation comes from a multi-order-parameter phase field model, developed by Braun et al.  and , for the description of crystalline interphase boundaries. In this, the smallness of $\epsilon$ 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 ,  does not apply. The existence of such a heteroclinic, and its dependence on $\epsilon$, is proved via a functional analytic approach.
Adv. Differential Equations Volume 12, Number 6 (2007), 623-668.
First available in Project Euclid: 18 December 2012
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Sourdis, C.; Fife, P. C. Existence of heteroclinic orbits for a corner layer problem in anisotropic interfaces. Adv. Differential Equations 12 (2007), no. 6, 623--668.https://projecteuclid.org/euclid.ade/1355867448