Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
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01 Jun 1964
TL;DR: In this article, the sufficiency of the above theorem without an assumption as to the sign of a(t) was established without any assumption on the degree of a (t) > 0, and a stronger asymptotic result for equation (1) under a stronger assumption was given.
Abstract: This theorem is an extension of a theorem of Atkinson [21. Theorem 1 of this paper establishes the sufficiency of the above theorem without an assumption as to the sign of a(t). A theorem somewhat like the theorem of Trench [3] is given in Theorem 2 but for a nonlinear equation. As an application of this theorem, a stronger asymptotic result (under a stronger assumption) for equation (1) is given in Theorem 3. Other theorems on the asymptotic behavior of (1) when a(t) > 0 are contained in [4 ]. THEOREM 1. If a(t) is continuous and
49 citations
TL;DR: In this paper, the problem of steady free convection in a porous medium adjacent to a horizontal impermeable heated surface, with wall temperature distribution w=∞+Aλ(0≤λ<2), for ≥0 and =∞ for <0, is investigated by the method of matched asymptotic expansions.
49 citations
48 citations
TL;DR: In this paper, a boundary-value problem for the Poisson equation in a thick junction is considered, where the boundary condition ∆ + eκ(ue)=0 is given on the lateral surfaces of the thin cylinders and the asymptotic analysis of this problem is performed as e à 0, i.e. when the number of thin cylinders infinitely increases and their thickness tends to zero.
Abstract: We consider a boundary-value problem for the Poisson equation in a thick junction Ωe, which is the union of a domain Ω0 and a large number of e-periodically situated thin curvilinear cylinders. The following nonlinear Robin boundary condition ∂νue + eκ(ue)=0 is given on the lateral surfaces of the thin cylinders. The asymptotic analysis of this problem is performed as e 0, i.e. when the number of the thin cylinders infinitely increases and their thickness tends to zero. We prove the convergence theorem and show that the nonlinear Robin boundary condition is transformed (as e 0) in the blow-up term of the corresponding ordinary differential equation in the region that is filled up by the thin cylinders in the limit passage. The convergence of the energy integral is proved as well. Using the method of matched asymptotic expansions, the approximation for the solution is constructed and the corresponding asymptotic error estimate in the Sobolev space H1(Ωe) is proved. Copyright © 2007 John Wiley & Sons, Ltd.
48 citations
TL;DR: In this paper, the authors present the distributional theory of asymptotic expansions for functions of one variable, where the multidimensional expansions are studied in the central part of the book.
Abstract: The purpose of this chapter is to present the distributional theory of asymptotic expansions for functions of one variable. This chapter and the next, where the multidimensional expansions are studied, are the central part of the book.
48 citations