Geodesic
A Nonlocal Problem Arising in the Study of Magneto-Elastic Interactions
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 197-221.

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The energy of magneto-elastic materials is described by a nonconvex functional. Three terms of the total free energy are taken into account: the exchange energy, the elastic energy and the magneto-elastic energy usually adopted for cubic crystals. We focus our attention to a one dimensional penalty problem and study the gradient flow of the associated type Ginzburg-Landau functional. We prove the existence and uniqueness of a classical solution which tends asymptotically for subsequences to a stationary point of the energy functional.
Si studia il funzionale non convesso che descrive l'energia di un materiale magneto-elastico. Sono considerati tre termini energetici: l'energia di scambio, l'energia elastica e l'energia magneto-elastica generalmente adottata per cristalli cubici. Si introduce un problema penalizzato monodimensionale e si studia il flusso di gradiente dell'associato funzionale del tipo Ginzburg-Landau. Si prova l'esistenza e la unicità di una soluzione classica che tende asintoticamente, per sottosuccessione, a un punto stazionario del funzionale dell'energia. 
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Chipot, M.; Shafrir, I.; Vergara Caffarelli, G. A Nonlocal Problem Arising in the Study of Magneto-Elastic Interactions. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 197-221. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_1_a7/

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