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 article, the authors study the complicated asymptotic character of a simple first-order differential equation, which involves a term with a low exponent of the dependent variable.
Abstract: We study the surprisingly complicated asymptotic character of a simple first-order differential equation, which involves a term with a low exponent of the dependent variable. While numerical solutions and straightforward asymptotic expansions indicate a clearly defined boundary layer type transition, we find that the correct asymptotic structure involves a hidden' boundary layer, and that a straightforward approach cannot discern this.
3 citations
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TL;DR: In this paper, the derivation of asymptotic expansions for functions of a certain class is studied, which satisfy a differential equation in a variablez and a recursion in a parametern and include most of the classical functions of Mathematical Physics.
Abstract: The paper deals with the derivation of asymptotic expansions for functions of a certain class. The functions concerned satisfy a differential equation in a variablez and a recursion in a parametern and include most of the classical functions of Mathematical Physics.
3 citations
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TL;DR: In this paper, various categories of problems are distinguished with different first approximation formulations, showing different degrees of non-linearity, through the asymptotic approach to elastic theory of beam-like structural elements.
Abstract: Through the asymptotic approach to elastic theory of beam-like structural elements, various categories of problems are distinguished with different first approximation formulations, showing different degrees of non-linearity.
3 citations
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TL;DR: In this paper, the authors studied the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries.
Abstract: We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.
3 citations
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01 Nov 1952TL;DR: In this paper, a simple theory about the boundedness and asymptotic equilibria of solutions of non-linear differential equations is developed. But this theory is not applicable to the case of nonlinear perturbations.
Abstract: TIlE aim of this paper is to develop a simple theory about the boundedness and asymptotic equilibria of solutions of non-linear differential equations. Norman Levinson ~ and Hermann WeyV considered the boundedness of solutions of perturbed linear systems where the perturbations could be majorised by linear functions. Aurel Wintner 3, 4 considered the problem of asymptotic equilibria subject to certain conditions. We shall investigat,e sufficient conditions for the boundedness of solutions of non-linear differential equations and obtain a generalisation of the results of Aurel Wintner about asymptotic equilibria. The method suggested here is shown to be applicable to the case of non-linear perturbations as well.
3 citations