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Nonlinear nonlocal evolution problems.

N.-H. ChangM. Chipot — 2003


We consider a class of nonlinear parabolic problems where the coefficients are depending on a weighted integral of the solution. We address the issues of existence, uniqueness, stationary solutions and in some cases asymptotic behaviour.

A Nonlocal Problem Arising in the Study of Magneto-Elastic Interactions

M. ChipotI. ShafrirG. Vergara Caffarelli — 2008

Bollettino dell'Unione Matematica Italiana

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...

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