A Nonlocal Problem Arising in the Study of Magneto-Elastic Interactions
M. Chipot, I. Shafrir, G. Vergara Caffarelli (2008)
Bollettino dell'Unione Matematica Italiana
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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...