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 method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number was proposed, based on the assumption that properties of global solutions of kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of extremas.
Abstract: We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here the Maximally-Efficient-Generation Approach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema. The general method is illustrated by the global asymptotic solution of the α2-dynamo problem in a slab. The nature of oscillatory solutions revealed earlier in numerical simulations and the reasons for the dominance of even magnetic modes in slab geometry are clarified. Applicability of the asymptotic solutions at moderate values of the asymptotic parameter is also discussed. We confirm this applicability u...
18 citations
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18 citations
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TL;DR: In this article, the authors studied the asymptotic behavior of solutions to the Korteweg-deVries-Burgers equation in the case when the initial data has different scaling factors at different scales.
Abstract: In this work we study the asymptotic behaviour of solutions to the Korteweg--deVries--Burgers equation in the case when the initial data has different asymptotic limits at $\pm\infty $ The method used is the one developed by Kawashima and Matsumura to discuss the asymptotic behaviour of travelling-wave solutions to Burgers equation
18 citations
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01 Feb 1996
TL;DR: In this paper, asymptotic problems for non-linear elliptic equations in cylindrical domains and homogenization problems are studied. But the authors focus on homogenisation problems.
Abstract: Preface 1. Asymptotic problems for non-linear elliptic equations 2. On the asymptotic behaviour of solutions of some non-linear elliptic equations in cylindrical domains 3. On the asymptotic behaviour of solutions of non-linear elliptic equations in a neighbourhood of a conic point of the boundary 4. On some homogenization problems Index.
18 citations