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On the asymptotic properties of a canonical diffraction integral.

Accepted version
Peer-reviewed

Type

Article

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Authors

Abrahams, I David 

Abstract

We introduce and study a new canonical integral, denoted I + - ε , depending on two complex parameters α 1 and α 2. It arises from the problem of wave diffraction by a quarter-plane and is heuristically constructed to capture the complex field near the tip and edges. We establish some region of analyticity of this integral in C 2 , and derive its rich asymptotic behaviour as |α 1 | and |α 2 | tend to infinity. We also study the decay properties of the function obtained from applying a specific double Cauchy integral operator to this integral. These results allow us to show that this integral shares all of the asymptotic properties expected from the key unknown function G +- arising when the quarter-plane diffraction problem is studied via a two-complex-variables Wiener-Hopf technique (see Assier & Abrahams, SIAM J. Appl. Math., in press). As a result, the integral I + - ε can be used to mimic the unknown function G +- and to build an efficient 'educated' approximation to the quarter-plane problem.

Description

Keywords

Cauchy integrals, Wiener–Hopf, diffraction, quarter-plane

Journal Title

Proc Math Phys Eng Sci

Conference Name

Journal ISSN

1364-5021
1471-2946

Volume Title

476

Publisher

The Royal Society

Rights

All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/K032208/1)
Engineering and Physical Sciences Research Council (EP/R014604/1)