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, a general dimensional analysis is applied to derive, in Euclidean space, the asymptotic behaviour of renormalised (subtracted-out) Feynman amplitudes A. The maximising subspaces for the bond of A are constructed and an explicit expression for the behaviour of A is given including both power and logarithmic coefficients.
Abstract: A general dimensional analysis is applied to derive, in Euclidean space, the asymptotic behaviour of renormalised (subtracted-out) Feynman amplitudes A. The maximising subspaces for the bond of A are constructed and an explicit expression for the behaviour of A is given including both power and logarithmic asymptotic coefficients. The analysis provides rules for obtaining the asymptotic expression for A when some (or all) of the external momenta become large, some (or all) become small, and some of the masses are led to approach zero. Examples are then worked out as illustrations of these rules.
7 citations
13 Oct 2017
TL;DR: In this article, the authors studied the asymptotic behavior of global solutions to the initial value problem for the generalized KdV-Burgers equation and showed that the solution to this equation converges to a self-similar solution to the Burgers equation.
Abstract: We study the asymptotic behavior of global solutions to the initial value problem for the generalized KdV-Burgers equation. One can expect that the solution to this equation converges to a self-similar solution to the Burgers equation, due to earlier works related to this problem. Actually, we obtain the optimal asymptotic rate similar to those results and the second asymptotic profile for the generalized KdV-Burgers equation.
7 citations
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TL;DR: In this paper, a numerical algorithm for solving the asymptotic stabilization problem by the initial data to a fixed hyperbolic point with a given rate is proposed and justified, which makes it possible to apply the results to a wide class of semidynamical systems including those corresponding to partial differential equations.
Abstract: A numerical algorithm for solving the asymptotic stabilization problem by the initial data to a fixed hyperbolic point with a given rate is proposed and justified. The stabilization problem is reduced to projecting the resolving operator of the given evolution process on a strongly stable manifold. This approach makes it possible to apply the results to a wide class of semidynamical systems including those corresponding to partial differential equations. By way of example, a numerical solution of the problem of the asymptotic stabilization of unstable trajectories of the two-dimensional Chafee-Infante equation in a circular domain by the boundary conditions is given.
7 citations
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TL;DR: In this article, the fundamental solution of a divergence operator of the following form is considered, and two types of asymptotics of are considered, i.e. as and at infinity.
Abstract: Let be the fundamental solution of a divergence operator of the following form: Two types of asymptotics of are considered in the paper: the asymptotic behavior at infinity, i.e. as , and the asymptotic behavior of at . In the first case, for operators with smooth, quasiperiodic coefficients the principal term of the asymptotic expression is found, and a power estimate of the remainder term is established. In the second case the principal term in the asymptotic expression for as is found for an operator with arbitrary bounded and measurable coefficients . These results are obtained by means of the concept of the -convergence of elliptic differential operators. Further, applications of the results are given to the asymptotics of the spectrum of the operator in a bounded domain .Bibliography: 13 titles.
7 citations
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TL;DR: In this article, an asymptotic solution of the magnetic induction equation in a given velocity field is constructed for large magnetic Reynolds numbers, and the expansion of the leading term of the equation is proved to be rigorously valid over a finite time interval.
Abstract: An asymptotic solution of the magnetic induction equation in a given velocity field is constructed for large magnetic Reynolds numbers. Initially localized distributions of the magnetic field are considered. The leading term of the asymptotics is found. The expansions are proved to be rigorously valid over a finite time interval. Estimates for the residuals are given. The results are illustrated by some examples: the Hubble flow with a linear dependence of the velocity on coordinates, and ABC type flows. The solutions in these cases are expressed in terms of elementary functions.
7 citations