Publication Cover
Applicable Analysis
An International Journal
Volume 60, 1996 - Issue 3-4
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Original Articles

On the asymptotic solution of a wave damping problem arising in lnhomogeneous media

Pages 327-340 | Received 01 Nov 1995, Published online: 02 May 2007
 

Abstract

In studying a wave damping problem in inhomogeneous media, the following equation arises:

This paper considers the asymptotic solution of the above equation for large complex values of u which is uniformly valid in x. Attention is focused on the solution which tends to zero as x tends to infinity and for values of u in the half plane Re(u) > 0. The results obtained are simply expressed in terms of the Macdonald type Bessel function Ku(x). Our method utilizes a relation between two types of the modified Bessel functions and a uniform asymptotic formula for Ku(x), and depends for its success on a novel method to obtain the uniform bounds for the Green function that arises in the reformulated integral equation.

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