On the Asymptotic Solution to a Class of Linear Integral Equations

We consider Fredholm integral equations of the first kind whose kernels are a function of the difference between two points times a large parameter. Conditions on the kernel are stated in terms of a function corresponding to a Wiener-Hopf factorization of the Fourier transform of the kernel. We give...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on applied mathematics 1988-04, Vol.48 (2), p.294-306
Main Author: Gautesen, A. K.
Format: Article
Language:English
Subjects:
Applied mathematics
Differential equations
Elastic waves
Exact sciences and technology
Factorization
Fourier transformations
Fourier transforms
Function theory, analysis
Integral equations
Integrals
Mathematical functions
Mathematical methods in physics
Physics
Plane waves
Sine function
Surface waves
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider Fredholm integral equations of the first kind whose kernels are a function of the difference between two points times a large parameter. Conditions on the kernel are stated in terms of a function corresponding to a Wiener-Hopf factorization of the Fourier transform of the kernel. We give the complete asymptotic expansions of the solution to the integral equations. As applications of our results, we consider the steady-state, acoustical scattering of a plane wave by both a hard strip and a soft strip. Our results are uniform with respect to the direction of incidence.
ISSN:0036-1399
1095-712X
DOI:10.1137/0148015