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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9 citations
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9 citations
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TL;DR: In this article, the authors give an outline of mathematical models of multi-structures based on an asymptotic analysis of a class of elliptic boundary value problems posed in singularly perturbed domains.
Abstract: This review paper gives an outline of mathematical models of multi-structures. The approach is based on an asymptotic analysis of a class of elliptic boundary value problems posed in singularly perturbed domains. A particular attention is given to formulation of the “junction conditions” to link different parts of the multi-structure. The paper also discusses a range of applications of this asymptotic theory in physics and mechanics.
9 citations
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TL;DR: In this paper, an extension of the method of asymptotic decompositions of vector fields with finite-time singularities was proposed, by applying the central extension technique of Poincar\'e to the dominant part of the vector field on approach to the singularity.
Abstract: We provide an extension of the method of asymptotic decompositions of vector fields with finite-time singularities by applying the central extension technique of Poincar\'e to the dominant part of the vector field on approach to the singularity. This leads to a bundle of fan-out asymptotic systems whose equilibria at infinity govern the dynamics of the asymptotic solutions of the original system. We show how this method can be useful to describe a single-fluid isotropic universe at the time of maximum expansion, and discuss possible relations of our results to structural stability and non-compact phase spaces.
9 citations
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TL;DR: First order asymptotics are presented in a general framework under minimal regularity conditions and for not necessarily nested models, and give sufficient and in a sense necessary conditions for asymPTotic normality of test statistics under alternative hypotheses.
9 citations