A Γ-Convergence Result for Thin Curved Films Bonded to a Fixed Substrate with a Noninterpenetration Constraint

Abstract : The behavior of a thin curved hyperelastic film bonded to a fixed substrate is described by an energy composed of a nonlinearly hyperelastic energy term and a debonding interfacial energy term. The author computes the Γ-limit of this energy under a noninterpenetration constraint that prohibits penetration of the film into the substrate without excluding contact between the

Existence and uniqueness of global solutions for the modified anisotropic 3D Navier-Stokes equations

We study a modified three-dimensional incompressible anisotropic Navier-Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a fluid obeys the Darcy-Forchheimer law instead of the classical Darcy law. We prove global in time existence and uniqueness of solutions without assuming the smallness condition on the initial data. This improves the result obtained for the classical 3D incompressible anisotropic Navier-Stokes equations.Comment: To appear in ESAIM: Mathematical Modelling and Numerical Analysi

Dimensional reduction for energies with linear growth involving the bending moment

A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.Comment: 26 page

A Γ\Gamma -convergence result for optimal design problems

In this paper, we derive the $\Gamma$-limit of some optimal material distribution problems as the exponent goes to infinity

Curved ferromagnetic thin films

On considère un film courbé mince ferromagnétique non soumis à un champ magnétique externe. Le comportement du film est décrit par une énergie dépendant de la magnétisation du film vérifiant la contrainte de saturation. Cette énergie se compose d'une partie d'énergie magnétostatique induite et d'un terme d'énergie ayant comme densité une fonction, comprenant l'énergie d'échange et l'énergie anisotrope. Nous étudions le comportement de cette énergie quand l'épaisseur du film courbé tend vers zéro. Nous prouvons avec des arguments de Γ-convergence que les minimiseurs de l'énergie totale convergent vers les minimiseurs d'une énergie locale dépendant d'une magnétisation bidimensionnelle.We consider a thin curved ferromagnetic film not submitted to an external magnetic field. The behavior of the film is described by an energy depending on the magnetization of the film verifying the saturation constraint. The energy is composed of an induced magnetostatic energy and an energy term with density including the exchange energy and the anisotropic energy. We study the behavior of this energy when the thickness of the curved film goes to zero. We show with Γ-convergence arguments that the minimizers of the free energy converge to the minimizers of a local energy depending on a two-dimensional magnetization.ou

A Γ\Gamma -convergence result for optimal design problems

In this paper, we derive the $\Gamma$-limit of some optimal material distribution problems as the exponent goes to infinity