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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: Bensoussan, Alain
Article Type: Other
Citation: Asymptotic Analysis, vol. 16, no. 2, pp. 85-85, 1998
Authors: , G.D.Raikov
Article Type: Research Article
Abstract: We consider the two‐dimensional Schrödinger operator with generically bounded magnetic field, perturbed by a scalar potential -gV , g \geq 0 being the coupling constant. We assume that V is non‐negative and decays rapidly at infinity (e.g., V({\mathbf x})\asymp \vert{\mathbf x}\vert^{-\alpha} , \alpha > 2 , as \vert{\mathbf x}\vert\rightarrow \infty ). We examine the asymptotic behaviour as g \rightarrow \infty of the eigenvalues situated in the gaps of the spectrum of the unperturbed operator.
Citation: Asymptotic Analysis, vol. 16, no. 2, pp. 87-98, 1998
Authors: Dauge, Monique | Gruais, Isabelle
Article Type: Research Article
Abstract: This paper is the last of a series of two, where we study the asymptotics of the displacement in a thin clamped plate as its thickness tends to 0 . In Part I, relying on the structure at infinity of the solutions of certain model problems posed on unbounded domains, we proved that the combination of a polynomial Ansatz (outer expansion) and of a boundary layer Ansatz (inner expansion) yields a complete multi‐scale asymptotics of the displacement and optimal estimates in energy norm. The “profiles” for the boundary layer terms are solutions of such model problems. In this paper, …adapting Saint‐Venant’s principle to our framework, we prove the results which we used in Part I. Investigating more precisely the structure of the boundary layer terms, we go further in the analysis performed in Part I: the introduction of edge layer terms along the intersections of the clamped face with the top and the bottom of the plate, respectively, allows estimates in higher order norms. These edge layer terms are constructed with the help of stable asymptotics, and are the singular parts of the boundary layer terms. As a by‐product of all these investigations, we obtain expansions and estimates for the stress tensor in various anisotropic norms, and also estimates in L^\infty ‐norm for the displacement field. Show more
Citation: Asymptotic Analysis, vol. 16, no. 2, pp. 99-124, 1998
Authors: Muñoz, Julio | Pedregal, Pablo
Article Type: Research Article
Abstract: A general approach to relaxation for an optimal design problem for plates is proposed. Generalized minimizers in terms of Young measures are found and an attempt to reduce the design variables needed for the description of these minimizers is pursued. We examine special representations of the convex hull of a particular curve in three space dimensions where its specific properties are exploited in a fundamental way in order to obtain different descriptions of generalized minimizers. We also find the optimal relaxation by further analyzing the features of that curve.
Citation: Asymptotic Analysis, vol. 16, no. 2, pp. 125-140, 1998
Authors: Bryan, Kurt | Vogelius, Michael
Article Type: Research Article
Abstract: We study the effective behaviour of a periodic array of microscopic cracks inside a homogeneous conductor. Special emphasis is placed on a rigorous study of the case in which the corresponding effective conductivity becomes nearly singular – due to the fact that adjacent cracks nearly touch. It is heuristically shown how thin clusters of such extremely close cracks may macroscopically appear as a single crack. These results have implications for our earlier work on impedance imaging.
Citation: Asymptotic Analysis, vol. 16, no. 2, pp. 141-179, 1998
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