### High-electric-field limit for the Vlasov–Maxwell–Fokker–Planck system

Mihai Bostan, Thierry Goudon (2008)

Annales de l'I.H.P. Analyse non linéaire

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Mihai Bostan, Thierry Goudon (2008)

Annales de l'I.H.P. Analyse non linéaire

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Khalid Benmlih, Otared Kavian (2008)

Annales de l'I.H.P. Analyse non linéaire

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Ping Zhang, Yuxi Zheng (2005)

Annales de l'I.H.P. Analyse non linéaire

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Fanghua Lin, Ping Zhang (2004-2005)

Séminaire Équations aux dérivées partielles

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In this paper, we study the semiclassical limit of the cubic nonlinear Schrödinger equation with the Neumann boundary condition in an exterior domain. We prove that before the formation of singularities in the limit system, the quantum density and the quantum momentum converge to the unique solution of the compressible Euler equation with the slip boundary condition as the scaling parameter approaches $0.$

Li, Jingna (2009)

Abstract and Applied Analysis

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Kévin Santugini-Repiquet (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the homogenization process of ferromagnetic multilayers in the presence of surface energies: super-exchange, also called interlayer exchange coupling, and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequence of extension operators for the multilayer geometry. First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction...

Giovanni Pisante (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies $$\phantom{\rule{-17.07164pt}{0ex}}{\mathcal{E}}_{\epsilon}\left(m\right)={\int}_{\Omega}\phi \left(x,\frac{x}{\epsilon},m\left(x\right)\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x-{\int}_{\Omega}{h}_{e}\left(x\right)\xb7m\left(x\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x+\frac{1}{2}{\int}_{{\mathbb{R}}^{3}}{\left|\nabla u\left(x\right)\right|}^{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$$ of a large ferromagnetic body is obtained.