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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01 Jul 1976
4 citations
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TL;DR: In this paper, a formal, uniformly valid, asymptotic expansion of the Klein-Gordon equation with spatially varying coefficients is obtained with the help of two families of rays, and involving four functions : two successive Bessel functions of integer order and two new functions which are called the diffraction functions.
Abstract: The signaling problem for the one dimensional Klein-Gordon equation with spatially varying coefficients is analyzed. A formal, uniformly valid, asymptotic expansion of the solution is obtained with the help of two families of rays, and involving four functions : two successive Bessel functions of integer order and two new functions which we call the diffraction functions. The validity of the expansion is established when the coefficients in the Klein-Gordon equation are constants, and the results are applied to a signaling problem for a class of acoustic wave guides.
4 citations
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4 citations
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TL;DR: In this article, the singularly perturbed linear evolution equations of resonance type are considered in a Banach space and the Hilbert and Chapman-Enskog algorithms for generating asymptotic solutions are presented and shown to lead to different results at each finite order of approximation.
4 citations
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TL;DR: For a class of weakly non-linear oscillations involving a small parameter e, the authors derived sufficient conditions for asymptotic correctness as ǫ ↓ 0 to be satisfied by formal asymPTotic solutions.
Abstract: For a class of weakly non-linear oscillations involving a small parameter e we determine asymptotic solutions as ɛ ↓ 0 which are uniformly valid on some time interval. First, we consider a general initial-value problem in IRn containing a small parameter ɛ. We derive sufficient conditions for asymptotic correctness as ɛ ↓ 0 to be satisfied by formal asymptotic solutions. Next, we consider for the original problem formal asymptotic solutions of a two-variable type. For this type of formal asymptotic solutions the conditions for asymptotic correctness take a form which is very useful in the subsequent development of a construction technique for asymptotic solutions.
4 citations