Advances in Differential Equations

Existence of heteroclinic orbits for a corner layer problem in anisotropic interfaces

P. C. Fife and C. Sourdis

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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. [5] and [11], 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 [6], [9] does not apply. The existence of such a heteroclinic, and its dependence on $\epsilon$, is proved via a functional analytic approach.

Article information

Adv. Differential Equations, Volume 12, Number 6 (2007), 623-668.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34E10: Perturbations, asymptotics
Secondary: 34C37: Homoclinic and heteroclinic solutions 37C29: Homoclinic and heteroclinic orbits 74N05: Crystals


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.

Export citation