Asymptotic Analysis - Volume 39, issue 1

Authors: Petcu, M.

Article Type: Research Article

Abstract: The aim of this article is to prove results of space and time regularity of solutions for the Primitive Equations of the ocean in space dimension two with periodic boundary conditions. It is shown that these solutions belong to a certain Gevrey class of functions which is a subset of real analytic functions.

Keywords: Gevrey regularity, primitive equations for the ocean, energy estimate, analyticity

Citation: Asymptotic Analysis, vol. 39, no. 1, pp. 1-13, 2004

Authors: Ganesh, S. Sivaji | Vanninathan, M.

Article Type: Research Article

Abstract: Periodic homogenization result for selfadjoint operators via Bloch wave method was obtained by Conca and Vanninathan in [12]. Even though the spectral tools used in [12] are not available in non‐selfadjoint case, it is possible to recover the complete homogenization result of Murat and Tartar in the periodic case through the Bloch wave method. A dominant Bloch mode is introduced and plays the key role in the homogenization process. It is also established that the remainder does not contribute in the homogenization process. This requires separation of scales between the dominant Bloch mode and the rest. This separation is proved …via a Poincaré‐type inequality. Further, the proof of homogenization theorem of [12] is simplified. Show more

Keywords: Bloch waves, homogenization

Citation: Asymptotic Analysis, vol. 39, no. 1, pp. 15-44, 2004

Authors: Damlamian, A. | Donato, P.

Article Type: Research Article

Abstract: In this paper we give a general iterative method for the homogenization of elliptic problems in perforated domains with finitely many periodic scales. It is derived from a more general result, where only one (the biggest) scale is assumed to be ε‐periodic. For the smaller scales, only H0 ‐convergence is assumed. In the case of finitely many periodic scales, explicit formulas for the homogenized operators are obtained.

Citation: Asymptotic Analysis, vol. 39, no. 1, pp. 45-60, 2004

Authors: Freddi, Lorenzo | Paroni, Roberto

Article Type: Research Article

Abstract: A variational limit defined on the space of one‐dimensional Young measures is obtained from three‐dimensional elasticity via dimension reduction. The physical requirement that the energy becomes infinite when the volume locally vanishes is taken into account. The rate at which it blows up characterizes the domain of the limit energy. The obtained limit problem uniquely determines the energy density of the elastic string.

Citation: Asymptotic Analysis, vol. 39, no. 1, pp. 61-89, 2004