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Onétudie le comportement asymptotique de la solution de l'´ equation de Laplace dans un domaine dont une partie de lafrontì ere est fortement oscillante. La motivation de ce travail est l'´ etude d'unécoulement longitudinal dans un domaine infini borné inférieurement par une paroi et supérieurement par une paroi rugueuse. Cettedernì ere est un plan… (More)

We consider the linearized elasticity system in a multidomain of R 3. This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius r ε. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and r ε tend to… (More)

We consider a thin multidomain of R 3 consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the second one with small thickness and given cross section. The first part of this paper is devoted to analyze, in this thin multidomain, a " static Landau-Lifshitz equation " , when the volumes of… (More)

This paper is composed of two parts. In the first part, via a reduction dimension method, we derive a one-dimensional minimization problem involving S 2 valued maps for a thin T-shaped multidomain. In the second one, we analyze this limit model.

We consider a thin multidomain of R N , N ≥ 2, consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the second one with small thickness and given cross section. In this multidomain we study the asymptotic behavior, when the volumes of the two cylinders vanish, of a Laplacian eigenvalue… (More)

In this paper, starting from the classical 3D micromagnetic energy, we determine, via an asymptotic analysis, the free energy of two joined ferromagnetic thin films. We distinguish different regimes depending on the limit of the ratio between the small thicknesses of the two films.

We study the asymptotic behaviour, as h tends to +∞, of the nonlinear system: −∆u h − u h + |u h | 2 u h = f in Ω h , Du h · ν = 0 on ∂Ω h , u h : Ω h → R 2 , in a varying domain Ω h in R 2. The boundary ∂Ω h contains an oscillating part like a comb with fine teeth periodically distributed in the first direction 0x 1 with period h −1 and thickness λh… (More)

We investigate the asymptotic behavior, as ε → 0, of the Kirchhoff-Love equation satisfied by the transverse displacement U ε of the middle surface Ω + ε ∪ Ω − ε (contained in the (x 1 , x 2)-coordinate plane) of a thin three-dimensional plate. The middle surface is composed of two domains. The first one Ω − ε is a thin strip with vanishing height h ε (in… (More)

We consider a thin multidomain of R 3 consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the second one with small thickness and given cross section. The first part of this paper is devoted to analyze, in this thin multidomain, a " static Landau–Lifshitz equation " , when the volumes of… (More)