Asymptotic Analysis - Volume 7, issue 2

Authors: Allaire, Grégoire | Murat, François

Article Type: Research Article

Abstract: We consider the homogenization of second-order elliptic equations with a Neumann boundary condition in open sets periodically perforated with holes of the size of the period. When the holes are isolated, Cioranescu and Saint Jean Paulin (1979) proved the convergence of the homogenization process. One of their main tool was the construction of an extension of the solution, which is uniformly bounded. In the present paper, we give a new proof of the convergence, which avoids the use of such an extension. The main advantage of our approach is that it generalizes the result of Cioranescu and Saint Jean Paulin …to the general case of periodic holes which may be not isolated (including, for example in three dimensions, the case of a domain perforated by interconnected cylinders). Show more

DOI: 10.3233/ASY-1993-7201

Citation: Asymptotic Analysis, vol. 7, no. 2, pp. 81-95, 1993

Authors: Petkov, Vesselin | Vodev, Georgi

Article Type: Research Article

Abstract: We obtain a new type of upper bounds on the number of scattering poles which allow to give some sufficent conditions for the Lax-Phillips conjecture (and also the modified one) to hold for a class of compactly supported hypoelliptic perturbations of the Laplace operator in Rn , n≥3 being odd.

DOI: 10.3233/ASY-1993-7202

Citation: Asymptotic Analysis, vol. 7, no. 2, pp. 97-104, 1993

Authors: Joseph, K.T.

Article Type: Research Article

Abstract: In this paper we study the Riemann problem for a 2×2 system of conservation laws, whose solution need not be real-valued functions, but may contain δ-measures concentrated along some curves. We consider a parabolic approximation of the Riemann problem and obtain an explicit formula. Then the solution of the Riemann problem is obtained as the limit of this approximate solution.

DOI: 10.3233/ASY-1993-7203

Citation: Asymptotic Analysis, vol. 7, no. 2, pp. 105-120, 1993

Authors: Balser, W. | Tovbis, A.

Article Type: Research Article

Abstract: Multisummability is a technique of assigning a sum to certain formal power series with zero radius of convergence. In this paper, those functions that occur as such sums are characterized. Furthermore, this result is applied in proving multisummability of iterated integrals; these are integrals which frequently occur, e.g., in proofs of the basic Asymptotic Existence Theorem for linear and nonlinear meromorphic differential equations.

DOI: 10.3233/ASY-1993-7204

Citation: Asymptotic Analysis, vol. 7, no. 2, pp. 121-127, 1993

Authors: Alvarez-Dios, J.A. | Viano, J.M.

Article Type: Research Article

Abstract: We use asymptotic techniques on a re-scaled three-dimensional linear elasticity model to justify and generalise models describing the elastic behaviour of rods, taking into account the nonhomogeneity and anisotropy of the material they are made of. General bending models for nonhomogeneous anisotropic rods are obtained as the limit of the tridimensional elasticity model when the cross section area tends to zero. We also include convergence results mathematically justifying the method. Next, by identification of second-order terms in the asymptotic expansion we obtain a general theory for transversally nonhomogeneous isotropic rods taking into account Timoshenko and Saint Venant's effects.

DOI: 10.3233/ASY-1993-7205

Citation: Asymptotic Analysis, vol. 7, no. 2, pp. 129-158, 1993