Asymptotic Analysis - Volume 2, issue 3

Authors: Stuwe, Hans-Christof | Werner, Peter

Article Type: Research Article

Abstract: We study the low-frequency asymptotics of the solutions of the exterior Robin problem for the reduced wave equation in two dimensions and of the time-independent Schrödinger equation in one and two dimensions with a nonnegative potential with compact support, by employing integral equation methods. Applications to time-dependent problems are indicated.

DOI: 10.3233/ASY-1989-2301

Citation: Asymptotic Analysis, vol. 2, no. 3, pp. 179-202, 1989

Authors: Allaire, Grégoire

Article Type: Research Article

Abstract: In this paper we prove the convergence of the homogenization process of the Stokes equations with Dirichlet boundary condition in a periodic porous medium. We consider here the case where the solid part of the porous medium is connected, and we generalize to this case the results obtained by Tartar (1980).

DOI: 10.3233/ASY-1989-2302

Citation: Asymptotic Analysis, vol. 2, no. 3, pp. 203-222, 1989

Authors: Trabucho, L. | Viaño, J.M.

Article Type: Research Article

Abstract: This work is a continuation of an earlier work by Bermudez and Viaño (1984) on the same subject. In fact, using the same asymptotic expansion in linear elastic beams we give a complete characterization of displacements, bending moments and shear forces of orders 0, 1 and 2. These results include a characterization of the stress field of order 0 and of the axial and shear stresses of order 1. An appropriate physical interpretation of these results, which is considered elsewhere, will allow us to derive and to justify, from a mathematical point of view, the most well-known classical extension, bending …and torsion theories for linear elastic beams, including the Bernoulli-Navier, Saint Venant, Timoshenko and Vlasov models. Show more

DOI: 10.3233/ASY-1989-2303

Citation: Asymptotic Analysis, vol. 2, no. 3, pp. 223-255, 1989