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The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.
Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
Authors: Golse, François | Martel, Valérie
Article Type: Research Article
Abstract: In the kinetic theory of gases, half‐space problems are important because they govern the behavior of correctors to the Hilbert expansion near the boundaries. This paper takes up the discussion in Coron et al., Comm. Pure Appl. Math. 41 (1988) by a different method, based on the index formula for Wiener–Hopf operators on the half‐line. This method leads naturally to a new result on analogues of Chandrasekhar’s H function, which does not seem easy to obtain by the energy method of Coron et al. (1988).
Citation: Asymptotic Analysis, vol. 21, no. 1, pp. 1-21, 1999
Authors: Ta‐tsien, Li | (Li Da‐qian), | Jinhai, Yan
Article Type: Research Article
Abstract: This paper deals with the limit behaviour of solutions to certain kinds of boundary value problems with equivalued surface on a domain with thin layer. Some applications are given in resistivity well‐logging, etc.
Keywords: Limit behaviour, boundary value problem with equivalued surface, boundary value problem with equivalued interface, resistivity well‐logging
Citation: Asymptotic Analysis, vol. 21, no. 1, pp. 23-35, 1999
Authors: Berlyand, Leonid
Article Type: Research Article
Abstract: We study a nonlinear homogenization problem in perforated domains for the Ginzburg–Landau functional with a surface energy integral term which was introduced in the theory of liquid crystals. Under certain conditions between the inclusion size and the order of the surface energy integral we compute the nonlinear homogenized problem and prove the convergence of the solutions. An additional relation between the domain size and physical parameters provides the uniqueness of the homogenized limit. Our proof is based on a variational approach and does not require strict periodicity of the perforated domains.
Keywords: Homogenization, Ginzburg–Landau functional, surface energy
Citation: Asymptotic Analysis, vol. 21, no. 1, pp. 37-59, 1999
Authors: Joshi, Mark S. | Sá Barreto, Antônio
Article Type: Research Article
Abstract: The problem of recovering the asymptotics of a short range perturbation of the Euclidean Laplacian on \mathbb{R}^n from fixed energy scattering data is studied. It is shown that for n \geq 3 the asymptotics of a magnetic potential are determined, modulo Gauge invariance, by its scattering matrix at a fixed non‐zero energy. This result also holds for a wide class of scattering manifolds.
Keywords: Scattering theory, conormal, Lagrangian
Citation: Asymptotic Analysis, vol. 21, no. 1, pp. 61-70, 1999
Authors: Irago, H. | Viaño, J.M.
Article Type: Research Article
Abstract: Let u(\varepsilon) be the rescaled three‐dimensional displacement field solution of the linear elastic model for a clamped prismatic straight rod {\varOmega}^\varepsilon having cross section with diameter of order \varepsilon , and let u^0 be the corresponding Bernoulli–Navier displacement. In this article we establish that the error \|u(\varepsilon)-u^0\|_{1,{\varOmega}} in the reference space [H^1({\varOmega})]^3 is of order \varepsilon^{1/2} . We mainly use an auxiliar corrector function and we prove that this estimation cannot be improved using other corrector functions of the same family.
Keywords: Asymptotic analysis, elastic rods, error estimations, Bernoulli–Navier model
Citation: Asymptotic Analysis, vol. 21, no. 1, pp. 71-87, 1999
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