Asymptotic Analysis - Volume 83, issue 4

Authors: Nayam, Al-hassem

Article Type: Research Article

Abstract: We consider the problem of the optimal location of a Dirichlet region in a d-dimensional domain Ω subjected to a given force f in order to minimize a given functional. We look for the optimal region among the class of all closed connected sets of assigned total length l. Then we let l tend to infinity and we look at the Γ-limit of a suitable rescaled functional, in order to get information of the asymptotic distribution of the optimal region.

Keywords: optimal network location, shape optimization, Γ-convergence

DOI: 10.3233/ASY-121156

Citation: Asymptotic Analysis, vol. 83, no. 4, pp. 285-302, 2013

Authors: Sasu, Adina Luminiţa | Sasu, Bogdan

Article Type: Research Article

Abstract: The aim of this paper is to present a new and a complete study concerning the asymptotic behavior of autonomous systems in terms of input–output techniques. We characterize the exponential dichotomy of autonomous systems modeled by C0 -semigroups in terms of admissibility type conditions, pointing out connections between the dichotomic splitting and the properties of the solutions of some associated control systems in certain function spaces. We deduce the structure and the uniqueness of the dichotomy projection and we obtain necessary and sufficient conditions for exponential dichotomy. Next, the main results are applied to the study of the stability and …expansiveness of autonomous systems on the half-line. Throughout the paper, we present several examples which motivate the techniques and clarify the relevance of the arguments and the generality of the obtained results. Show more

Keywords: autonomous system, dichotomy, stability, expansiveness

DOI: 10.3233/ASY-121161

Citation: Asymptotic Analysis, vol. 83, no. 4, pp. 303-329, 2013

Authors: Berezhnyi, Maksym | Khruslov, Eugen

Article Type: Research Article

Abstract: A viscous incompressible fluid with a large number of small axially symmetric solid particles is considered. It is assumed that the particles are identically oriented and under the influence of the fluid move translationally or rotate around a symmetry axis with the direction of their symmetry axes unchanged. The asymptotic behavior of oscillations of the system is studied, when the diameters of particles and distances between the nearest particles are decreased. The equations, describing the homogenized model of the system, are derived. It is shown that the homogenized equations correspond to a non-standard hydrodynamics. Namely, the homogenized stress tensor linearly …depends not only on the strain tensor but also on the rotation tensor. Show more

Keywords: microstructure, suspension, anisotropic material, inhomogeneous material, viscous incompressible fluid, asymmetric hydrodynamics, asymptotic analysis

DOI: 10.3233/ASY-131162

Citation: Asymptotic Analysis, vol. 83, no. 4, pp. 331-353, 2013

Authors: Lü, Qi | Yin, Zhongqi

Article Type: Research Article

Abstract: In this paper, we obtain the L∞ -null controllability of the parabolic equation with equivalued surface boundary conditions in Ω×[0,T]. The control is supported in the product of an open subset of Ω and a subset of [0,T] with positive measure. The main result is obtained by the method of Lebeau–Robbiano iteration, based on a new estimate for partial sum of the eigenfunctions of the elliptic operator with equivalued surface boundary conditions.

Keywords: L^∞-null controllability, parabolic equation, equivalued surface boundary condition, Lebeau–Robbiano iteration

DOI: 10.3233/ASY-131167

Citation: Asymptotic Analysis, vol. 83, no. 4, pp. 355-378, 2013

Article Type: Other

Citation: Asymptotic Analysis, vol. 83, no. 4, pp. 379-380, 2013