## 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

P. C. Fife and C. Sourdis

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 18 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1355867448

**Mathematical Reviews number (MathSciNet)**

MR2319451

**Zentralblatt MATH identifier**

1157.34047

**Subjects**

Primary: 34E10: Perturbations, asymptotics

Secondary: 34C37: Homoclinic and heteroclinic solutions 37C29: Homoclinic and heteroclinic orbits 74N05: Crystals

#### Citation

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