LUNA LAYNEZ , Manuel

En la Memoria se introduce un nuevo método para estudiar el comportamiento asintótico de las soluciones de problemas en ecuaciones en derivadas parciales, planteados sobre estructuras reticuladas dependientes de varios parámetros. Se trata de una adaptación original ... de un método de T.Arbogast, J. Douglas, U. Hornung para el tratamiento de...

In this paper we study the asymptotic behavior of the solution of an anisotropic, heterogeneous, linearized elasticity system in a thin cylinder (a beam). The beam is fixed (homogeneous Dirichlet boundary condition) on the whole of one of its extremities but only on several small fixing sets on the other extremity; on the remainder of the...

Comportement asymptotique de problèmes de diffusion posés dans un domaine formé de deux cylindres de diamètres et longueurs différentes. Nous étudions le comportement asymptotique de la solution d'un problème de diffusion posé sur l'union d'un cylindre de petit diamètre et de longueur fixe et d'un autre cylindre de longueur et de diamètre...

Estudiamos el comportamiento asintótico de una viga elástica delgada cuando su anchura, ε, tiende a cero. La viga está fijada en la totalidad de una de sus bases, mientras que en la otra, sólo lo está en la unión de N pequeñas zonas de talla εrε , r ε tendiendo a cero. Sobre el resto de la frontera se impone una condición de Neumann. El...

Nous étudions le comportement asymptotique de la solution d'un problème d'élasticité linéaire anisotrope et hétérogène dans un cylindre dont le diamètre ε tend vers zéro. Le cylindre est fixé (condition de Dirichlet homogène) sur la totalité de l'une de ses extrémités, mais seulement sur une petite partie (de taille εrε) de l'autre base ; sur...

In this paper we review some recent results concerning the study of the asymptotic behavior of viscous fluids in rough domains assuming Navier boundary conditions on the rough boundary. Our main interest is to study the relation between both the adherence and the Navier boundary conditions in the case of a boundary with weak rugosities. We show...

For a fixed bounded open set Ω ⊂ RN , a sequence of open sets Ωn ⊂ Ω and a sequence of sets Γn ⊂ ∂Ω ∩ ∂Ωn, we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on Ωn, satisfying Neumann boundary conditions on Γn and Dirichlet boundary conditions on ∂Ωn \ Γn. We obtain a representation of the limit problem which...

In order to study the asymptotic behavior of a fluid in a domain of small thickness $\ep$, it is common to use that the norm of the pressure $p_\ep$ in $L^q$, $q>1$, is smaller than $C\|\nabla p_\ep\|_{W^{-1,q}}/\ep$. Our purpose in the present paper is to improve this estimate by showing that in fact $p_\ep$ can be decomposed as the sum of two...

On considère un fluide visqueux de faible épaisseur ε sur un fond rugueux Γε, périodique de période rε et amplitude δε, δε rε ε, où on impose la condition de glissement. Quand ε converge vers zéro on obtient un système de type Reynolds qui dépend de la limite λ de (δε √ε )/(rε √rε ). Si λ = +∞, le fluide se comporte comme si on aurait imposé la...

We study the asymptotic behavior of the solutions of the Navier–Stokes system in a thin domain Ωε of thickness ε satisfying the Navier boundary condition on a periodic rough set Γε ⊂ ∂Ωε of period rε and amplitude δε, with δε rε ε. We prove that the limit behavior as ε goes to zero depends on the limit λ of δεε 1 2 /r 3 2 ε . Namely, if λ =...

This work is devoted to the homogenization of the anisotropic, linearized elasticity system posed on thin reticulated structures involving several parameters. We show that the result depends on the relative size of the parameters. In every case, we obtain a limit problem where both the microscopic and macroscopic scales appear together. From...

On considère un fluide visqueux de faible épaisseur ε sur un fond rugueux Γε, périodique de période rε et amplitude δε, δε rε ε, où on impose la condition de glissement. Quand ε converge vers zéro on obtient un système de type Reynolds qui dépend de la limite λ de (δε √ ε )/(rε √ rε ). Si λ=+∞, le fluide se comporte comme si on aurait...

The present paper deals with the asymptotic behavior of equi-coercive sequences {Fn} of nonlinear functionals defined over vector-valued functions in W1,p 0 (Ω)M , where p > 1, M ≥ 1, and Ω is a bounded open set of RN , N ≥ 2. The strongly local energy density Fn(·, Du) of the functional Fn satisfies a Lipschitz condition with respect to the...

We address the numerical approximation by finite-element methods of an optimal design problem for a two phase material in one space dimension. This problem, in the continuous setting, due to high frequency oscillations, often does not have a classical solution, and a relaxed formulation is needed to ensure existence. On the contrary, the...

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