Asymptotic Analysis - Volume 9, issue 4

Authors: Ta-Tsien, Li | Rodrigues, J.E | Chen, Zhu

Article Type: Research Article

Abstract: The limit behaviour of solutions to a class of non-linear and non-local elliptic boundary value problems, with respect to the shrinking of the equivalued surface, is obtained by means of the theory of boundary value problems for second order linear elliptic equations.

DOI: 10.3233/ASY-1994-9401

Citation: Asymptotic Analysis, vol. 9, no. 4, pp. 297-310, 1994

Authors: Sab, K.

Article Type: Research Article

Abstract: The homogenization of non-linear elastic media and elasto-piastic media is investigated. It is shown that the results established for periodic media hold also for statistically homogeneous ergodic (S.H.E.) media. The homogenization scheme is based on (i) — a formal analogy between periodic media and S.H.E. media, and, (ii) — the study of the duality in S.H.E. non-linear media. “Explicit” direct and dual definitions of the homogenized properties are provided and illustrated by an example.

DOI: 10.3233/ASY-1994-9402

Citation: Asymptotic Analysis, vol. 9, no. 4, pp. 311-336, 1994

Authors: Nandakumar, A.K.

Article Type: Research Article

Abstract: In this paper, we study the homogenization of eigenvalue problem associated with the elasticity system in a periodically (with period ε>0, a small parameter) perforated domain with tiny holes. The critical size of the holes aε is given by aε =C0 εN/N−2 if N≥3 and aε =exp (−C0 /ε2 ) if N=2, where C0 is a constant and N is the dimension. We will study the above eigenvalue problem as ε→0 and eigenvalues and eigenvectors.

DOI: 10.3233/ASY-1994-9403

Citation: Asymptotic Analysis, vol. 9, no. 4, pp. 337-358, 1994

Authors: Bourgeat, Alain | Mikelić, Andro

Article Type: Research Article

Abstract: We consider the hyperbolic-elliptic coupled nonlinear system describing two-phase immiscible flows, with neglected capillary pressure, through a one-dimensional porous medium. We prove the existence and uniqueness of an entropy solution for data corresponding to the solution with discontinuities in saturations. Then we study the homogenization of this system when the permeability and porosity are rapidly oscillating. We get the stability of our coupled system, due to the very special underlying structure of this system in one dimension. Finally we discuss the behavior of the system with oscillatory initial saturation. This result also contains the homogenization of two-component miscible flow in …a one-dimensional porous medium, without any dispersion term, as a special case. Show more

DOI: 10.3233/ASY-1994-9404

Citation: Asymptotic Analysis, vol. 9, no. 4, pp. 359-380, 1994

Authors: Marchetti, Charles

Article Type: Research Article

Abstract: We consider the linear filtering problem with a small observation noise. We approximate the signal and its estimation with asymptotic expansions (see [6] and [7]).

DOI: 10.3233/ASY-1994-9405

Citation: Asymptotic Analysis, vol. 9, no. 4, pp. 381-395, 1994

Article Type: Other

Citation: Asymptotic Analysis, vol. 9, no. 4, pp. 397-397, 1994