Displaying similar documents to “On homogenization of non-divergence form partial difference equations.”

Néel and Cross-Tie wall energies for planar micromagnetic configurations

François Alouges, Tristan Rivière, Sylvia Serfaty (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We study a two-dimensional model for micromagnetics, which consists in an energy functional over S 2 -valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps...

A note on asymptotic expansion for a periodic boundary condition

Ján Filo (1998)

Archivum Mathematicum

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The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet–Neuman boundary conditions with the period going to zero in 3 D.