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: In this paper, the authors investigated boundary value and spectral problems for an elliptic differential equation with rapidly oscillating coefficients in a thin perforated region with rapidly changing thickness and described algorithms for solutions of such problems in thin regions with different limiting dimensions.
Abstract: Boundary value and spectral problems for an elliptic differential equation with rapidly oscillating coefficients in a thin perforated region with rapidly changing thickness are investigated. Descriptions of asymptotic algorithms for solutions of such problems in thin regions with different limiting dimensions are combined. For a mixed inhomogeneous boundary value problem a corrector is constructed and an asymptotic estimate in the corresponding Sobolev space is established. Asymptotic bounds for eigenvalues and eigenfunctions of the Neumann spectral problems are also found. Full asymptotic expansions for the eigenvalues and eigenfunctions are constructed under certain symmetry assumptions about the structure of the thin perforated region and the coefficients of the equations. Bibliography: 21 titles.
14 citations
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TL;DR: In this article, a systematic comparison of the time-dependent and time-independent approaches to the asymptotic analysis of some operator evolution equations in the weak or singular coupling limits is presented.
14 citations
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TL;DR: In this article, an approach to conditional inference for nonergodic stochastic process models by considering asymptotic properties was developed, and the context for most of the analysis is that of Le Cam's LAMN theory.
14 citations
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TL;DR: In this article, the global asymptotic stability of the equilibrium point for the fractional difference equation was studied and the stability was shown to be robust to perturbations.
Abstract: We study the global asymptotic stability of the equilibrium point for the fractional difference equation 𝑥𝑛
14 citations
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01 Jun 1999TL;DR: In this article, the asymptotics behavior of solutions of the Becker-Doring cluster equations is determined for cases in which coagulation dominates fragmentation, and it is shown that all non-zero solutions tend weak* to zero.
Abstract: The asymptotics behaviour of solutions of the Becker-Doring cluster equations is determined for cases in which coagulation dominates fragmentation. We show that all non-zero solutions tend weak* to zero.
14 citations