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Néel and Cross-Tie wall energies for planar micromagnetic configurations

François Alouges, Tristan Rivière, Sylvia Serfaty (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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 of the limit....

Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations

François Alouges, Tristan Rivière, Sylvia Serfaty (2010)

ESAIM: Control, Optimisation and Calculus of Variations


We study a two-dimensional model for micromagnetics, which consists in an energy functional over S2-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 of the limit....

Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces

Mihai Mihăilescu, Vicenţiu Rădulescu (2008)

Annales de l’institut Fourier

We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.

New results on the Burgers and the linear heat equations in unbounded domains.

J.I. Díaz, S. González (2005)

RACSAM

We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, as, e.g. (0 +∞), and the solution is unique without prescribing its behaviour at infinity. We also consider the associate stationary problem. Finally, some applications to the linear heat equation with boundary conditions of Robin type are also given.

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