Geodesic
Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries
Nicholas D. Alikakos1 ; Paul C. Fife2 ; Giorgio Fusco3 ; C. Sourdis1
1University of Athens, Greece
2University of Utah, Salt Lake City, USA
3Università degli Studi dell'Aquila, Italy
Interfaces and free boundaries, Tome 8 (2006) no. 2, pp. 159-183

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DOI

Mathematically, the problem considered here is that of heteroclinic connections for a system of two second order differential equations of Hamiltonian type, in which a small parameter ε conveys a singular perturbation. The motivation comes from a multi-order-parameter phase field model developed by Braun et al [5] and [22] for the description of crystalline interphase boundaries. In this, the smallness of ε is related to large anisotropy. The existence of such a heteroclinic, and its dependence on ε, is proved. In addition, its robustness is investigated by establishing its spectral stability.
DOI : 10.4171/ifb/139
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Nicholas D. Alikakos  1   ; Paul C. Fife  2   ; Giorgio Fusco  3   ; C. Sourdis  1

1 University of Athens, Greece
2 University of Utah, Salt Lake City, USA
3 Università degli Studi dell'Aquila, Italy 
Nicholas D. Alikakos; Paul C. Fife; Giorgio Fusco; C. Sourdis. Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries. Interfaces and free boundaries, Tome 8 (2006) no. 2, pp. 159-183. doi: 10.4171/ifb/139
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     title = {Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries},
     journal = {Interfaces and free boundaries},
     pages = {159--183},
     year = {2006},
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