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2007 Existence of heteroclinic orbits for a corner layer problem in anisotropic interfaces
P. C. Fife, C. Sourdis
Adv. Differential Equations 12(6): 623-668 (2007). DOI: 10.57262/ade/1355867448


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.


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P. C. Fife. C. Sourdis. "Existence of heteroclinic orbits for a corner layer problem in anisotropic interfaces." Adv. Differential Equations 12 (6) 623 - 668, 2007.


Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1157.34047
MathSciNet: MR2319451
Digital Object Identifier: 10.57262/ade/1355867448

Primary: 34E10
Secondary: 34C37 , 37C29 , 74N05

Rights: Copyright © 2007 Khayyam Publishing, Inc.


Vol.12 • No. 6 • 2007
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