Asymptotic Analysis - Volume 74, issue 3-4

Authors: Anza Hafsa, Omar | Leghmizi, Mohamed Lamine | Mandallena, Jean-Philippe

Article Type: Research Article

Abstract: We study homogenization by Γ-convergence of functionals of type ∫Ω W(x/ε,∇ϕ(x)) dx, where Omega⊂RN is a bounded open set, ϕ∈W1,p (Omega;Rm ) and p>1, when the 1-periodic integrand W :RN ×Mm×N →[0,+∞] is not of p-polynomial growth. Our homogenization technique can be applied when m=N and W has a singular behavior of type W(x,ξ)→+∞ as det ξ→0. However, our technique is not consistent with the constraint W(x,ξ)=+∞ if and only if det ξ≤0.

Keywords: homogenization, Gamma-convergence, singular integrand, determinant constraints type, hyperelasticity

DOI: 10.3233/ASY-2011-1042

Citation: Asymptotic Analysis, vol. 74, no. 3-4, pp. 123-134, 2011

Authors: Perjan, Andrei | Rusu, Galina

Article Type: Research Article

Abstract: We study the behavior of solutions to the problem ε(u″ε (t)+A1 uε (t))+u′ε (t)+A0 uε (t)+B(uε (t))=fε (t), t∈(0,T], uε (0)=u0ε , u′ε (0)=u1ε , in the Hilbert space H as ε→0, where A1 , A0 are two linear self-adjoint operators and B is a Lipschitzian operator.

Keywords: singular perturbation, abstract second-order Cauchy problem, boundary layer function, a priori estimate

DOI: 10.3233/ASY-2011-1043

Citation: Asymptotic Analysis, vol. 74, no. 3-4, pp. 135-165, 2011

Authors: Blasselle, A. | Griso, G.

Article Type: Research Article

Abstract: The skin is made of three main layers which are, from the top to the bottom: the epidermis, the dermis and the hypodermis. We consider the dermis as made of a Stokes fluid interacting with a periodic network of elastic fibers, assumed to obey the linearized elasticity law of behaviour. Above and below, the epidermis and the hypodermis are elastic solids. As the dimension of the thickness is very small compared to the two others, we assume periodic boundary conditions in those two planar directions. We study the 3d fluid–structure interaction system in a first part, and in a second …part, we make the characteric size of the periodic element of the network go to zero in order to find an homogenized law for the whole skin. Starting from linear elastic materials, we find a viscoelastic law at the limit. Show more

Keywords: fluid–structure interaction, periodic unfolding, homogenization

DOI: 10.3233/ASY-2011-1049

Citation: Asymptotic Analysis, vol. 74, no. 3-4, pp. 167-198, 2011

Authors: Korotyaev, Evgeny

Article Type: Research Article

Abstract: We consider the Schrödinger operator Hy=−y″+(p+q)y with a periodic potential p plus a compactly supported potential q on the real line. The spectrum of H consists of an absolutely continuous part plus a finite number of simple eigenvalues below the spectrum and in each spectral gap γn ≠∅,n≥1. We prove the following results: (1) the distribution of resonances in the disk with large radius is determined, (2) the asymptotics of eigenvalues and antibound states are determined at high energy gaps, (3) if H has infinitely many open gaps in the continuous spectrum, then for any sequence (κ)1 ∞ ,κn ∈{0,2}, …there exists a compactly supported potential q with ∫R q dx=0 such that H has κn eigenvalues and 2−κn antibound states (resonances) in each gap γn for n large enough. Show more

Keywords: resonances, scattering, periodic potential, S-matrix

DOI: 10.3233/ASY-2011-1050

Citation: Asymptotic Analysis, vol. 74, no. 3-4, pp. 199-227, 2011

Authors: Matei, Basarab | Meignen, Sylvain | Zakharova, Anastasia

Article Type: Research Article

Abstract: We study in this paper non-linear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on the contractivity of the associated scheme for the differences. In particular, we show the regularity of the limit function, in Lp and Sobolev spaces.

Keywords: non-linear subdivision scheme, convergence of subdivision schemes, box splines

DOI: 10.3233/ASY-2011-1052

Citation: Asymptotic Analysis, vol. 74, no. 3-4, pp. 229-247, 2011

Article Type: Other

Citation: Asymptotic Analysis, vol. 74, no. 3-4, pp. 249-249, 2011