Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: The problem of optimal control of solutions of an elliptic equation in a domain with a small cavity is discussed in this article, where uniform asymptotic formulae for the solutions are obtained up to an arbitrary degree of the small parameter by the method of matching asymPTotic expansions.
Abstract: The problem of optimal control of solutions of an elliptic equation in a domain with a small cavity is discussed. Uniform asymptotic formulae for the solutions are obtained up to an arbitrary degree of the small parameter by the method of matching asymptotic expansions. Other aspects of the same problem have been considered by Kapustyan.
11 citations
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TL;DR: In this article, regular and singular asymptotic methods are applied to one-and two-dimensional integral equations of the first kind with irregular kernels that arise in the treatment of various 2D axisymmetric and 3D problems in contact mechanics.
11 citations
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TL;DR: In this paper, a solution is obtained using uniform asymptotic formulae along with semiclassic methods, based on Olver's theory (Asymptotics and Special Functions, Academic Press, New York, 1974).
Abstract: This work deals with the problem of the calculation of the radial spheroidal functions. A solution is obtained using uniform asymptotic formulae along with semiclassic methods. The present uniform asymptotic method is based on Olver's theory (Asymptotics and Special Functions, Academic Press, New York, 1974) to asymptotic solutions of the differential equations. Here we show that it is possible to accurately interpolate the spheroidal radial function in the real plane using Airy's functions.
11 citations