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 regularization of a singularity with respect to a parameter is derived by means of an extension of the original operator and subsequent application of perturbation theory in an unbounded space, and used to solve an extended problem asymptotically.
Abstract: In this paper the regularization of a singularity with respect to a parameter is derived by means of an extension of the original operator and subsequent application of perturbation theory in an unbounded space, and used to solve an extended problem asymptotically. It is proved that this asymptotic solution is unique. An appropriate restriction of the asymptotic solution thus obtained will be an asymptotic solution of the original problem; this restriction is also unique. The theory of this method is illustrated by an example of an ordinary linear system of general form.
3 citations
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TL;DR: In this article, an overview of recent development in asymptotic analysis of fields in multi-structures is presented. But the analysis of time-dependent fields in 1D-3D multi-Structures is not discussed.
Abstract: This paper contains an overview of recent development in asymptotic analysis of fields in multi-structures. We begin with simple examples of scalar dynamic problems in two dimensions, and then present analysis of time-dependent fields in 1D-3D multi-structures. The asymptotic results, presented here, are based on the method of compound asymptotic expansions. Copyright (C) 2000 John Wiley & Sons, Ltd.
3 citations
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TL;DR: In this article, the boundary asymptotic behavior of solutions for weighted -Laplacian equations that take infinite value on a bounded domain is proved. But the boundary is not defined.
Abstract: The goal of this paper is to prove the boundary asymptotic behavior of solutions for weighted -Laplacian equations that take infinite value on a bounded domain.
3 citations
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TL;DR: In this paper, asymptotic expansions are obtained which describe the wave behaviour of particles, where a new variable (action) is introduced where a small parameter emerges as a constant ratio for the highest derivative.
Abstract: In this paper asymptotic expansions are obtained which describe the wave behaviour of particles. The essence of the method lies in the fact that a new variable (action) is introduced where a small parameter emerges as a constant ratio for the highest derivative. In this case it is convenient to investigate equations of wave mechanics with the help of a single asymptotic method. The new variable is introduced in order to obtain the necessary equation of the characteristics. Section 1 contains necessary information about the asymptotic method. In Section 2 on the basis of physical considerations the wave equations are given in five-dimensional form with action as the fifth coordinate. In Section 3 an asymptotic expansion in h is obtained and a Cauchy problem (dispersion problem) is solved. In Section 4 a connection between the asymptotic expansion and perturbation theory is established and it is shown that the series in perturbation theory so constructed is part of some asymptotic series. A series of perturbation theory, as we can easily see, is to some extent a classical limit, when e and → 0, so that e 2 / c = const. In Section 5 it is shown that, in the case of Schrodinger' s equation, on the basis of the formulae obtained, a bounded wave impulse moves in accordance with equations which, in the limit of an exact impulse, are the Hamiltonian equations of classical dynamics. Also this case is equivalent to the case when → 0. The formulae obtained in Section 5 generalize Ehrenfest' s theorem, and the method enables us to calculate any dynamical variables which characterize the wave behaviour of the particles. Here we show that the statistical explanation of ordinary quantum mechanics can be avoided.
3 citations