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, the authors investigated the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction.
Abstract: The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic problems by Chipot and Rougirel, where the force functions are considered on the cross section of domains, we prove the non-local counterpart of their result.
Furthermore, recently Yeressian established a weighted estimate for solutions of nonlocal Dirichlet problems which exhibit the asymptotic behavior. The case whens= 1=2 was also treated as an example to show how the weighted estimate might be used to achieve the asymptotic behavior. In this article, we extend this result to each order between 0 and 1.
9 citations
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TL;DR: For the two-level version of boundary integral equations applied to the analysis of oscillations of composite thin-shelled constructions in an acoustic medium, asymptotic analysis and simplification of equations in several characteristic excitation bands is carried out within the framework of the plane problem.
8 citations
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8 citations
01 Jan 2008
TL;DR: In this article, the authors studied the asymptotic behavior of solutions of a dissipative plate equation in R N with periodic coecients and proved that the solutions for the linear model behave as the homogenized heat kernel.
Abstract: In this work we study the asymptotic behavior of solutions of a dissipative plate equation in R N with periodic coecients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as t ! 1. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.
8 citations
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01 Jan 1988TL;DR: In this article, the authors pointed out that an estimator, though asymptotically much less efficient than another, may still have much greater probability concentration than the latter.
Abstract: Partly of an expository nature this note brings out the fact that an estimator, though asymptotically much less efficient (in the classical sense) than another, may yet have much greater probability concentration (as defined in this article) than the latter.
8 citations