Asymptotic Analysis - Volume 41, issue 2

Authors: Joshi, M.S. | Lionheart, W.R.B.

Article Type: Research Article

Abstract: We show that the full symbol of the Dirichlet to Neumann map of the k‐form Laplace's equation on a Riemannian manifold (of dimension greater than 2) with boundary determines the full Taylor series, at the boundary, of the metric. This extends the result of Lee and Uhlmann for the case k=0. The proof avoids the computation of the full symbol by using the calculus of pseudo‐differential operators parametrized by a boundary normal coordinate and recursively calculating the principal symbol of the difference of boundary operators.

Citation: Asymptotic Analysis, vol. 41, no. 2, pp. 93-106, 2005

Authors: Laptev, A. | Safronov, O.

Article Type: Research Article

Abstract: We obtain an asymptotic formula for the number of negative eigenvalues of a class of two‐dimensional Schrödinger operators with small magnetic fields. This number increases as a coupling constant of the magnetic field tends to zero.

Citation: Asymptotic Analysis, vol. 41, no. 2, pp. 107-117, 2005

Authors: Ammari, Habib | Kang, Hyeonbae | Touibi, Karim

Article Type: Research Article

Abstract: In this paper we present mathematically rigorous derivations of asymptotic expansions of the effective electrical conductivity of periodic dilute composites in terms of the volume fraction occupied by the inclusions. Our derivations are based on layer potential techniques, and valid for high contrast mixtures and inclusions with Lipschitz boundaries. They are motivated by the practically important inverse problem of determining the volume fraction of a suspension of complicated shaped particles from boundary measurements of voltage potentials.

Keywords: effective properties, composite materials, layer potentials, generalized polarization tensors

Citation: Asymptotic Analysis, vol. 41, no. 2, pp. 119-140, 2005

Authors: Peng, Yue‐Jun | Wang, Ya‐Guang

Article Type: Research Article

Abstract: In this paper, we study the convergence of time‐dependent Euler–Poisson equations to incompressible type Euler equations via the quasi‐neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and the symmetric hyperbolic property of the systems are used to justify the convergence of the limit.

Keywords: Euler–Poisson equations, incompressible Euler equations, quasi‐neutral limit, asymptotic expansion and justification

Citation: Asymptotic Analysis, vol. 41, no. 2, pp. 141-160, 2005

Authors: De Maio, U. | Mel'nyk, T.A.

Article Type: Research Article

Abstract: In this paper we study a mixed boundary value problem for the Poisson equation in a multi‐structure Ωε , which is the union of a domain Ω0 and a large number N of ε‐periodically situated thin rings with variable thickness of order ε=𝒪(N−1 ). By using some special extension operator, we prove a convergence theorem as ε→0 and investigate the asymptotic behaviour of the solution under the Robin conditions on the boundaries of the thin rings.

Keywords: homogenization, extension operator, thick multi‐structure

Citation: Asymptotic Analysis, vol. 41, no. 2, pp. 161-177, 2005

Authors: González Vieli, Francisco Javier

Article Type: Research Article

Abstract: The rate of convergence, at a point x, of the Fourier integral of the indicator function of a regular plane domain U has been investigated by Popov [Russian Math. Surveys 52 (1997), 73–145] and by Pinsky and Taylor [J. Fourier Anal. Appl. 3 (1997), 647–703] for x not on the boundary $\curpartial U$ of U; they have shown that the larger the maximal order of contact of $\curpartial U$ with the circles centered at x, the slower the convergence. We show here that Popov's approach, which uses the method of stationary phase, can be extended to …the case x on the boundary $\curpartial U$ , giving exactly the same relation between rate of convergence and maximal order of contact. Show more

Keywords: Fourier inversion, indicator function, rate of convergence, order of contact

Citation: Asymptotic Analysis, vol. 41, no. 2, pp. 179-187, 2005