SOLVING A DUAL INTEGRAL EQUATION INVOLVING FOURIER TRANSFORMS ENCOUNTERED IN A CRACK PROBLEMS FOR FRACTURE ELASTIC MATERIALS

Abstract

The aim of the present work is to consider a mixed boundary value problem in a strip related to cracks of fracture materials. By the Fourier transform, the problem are reduced to studying a dual integral equations on one edge of the strip. The uniqueness and existence theorems of solution of dual integral equation are established in appropriate Sobolev spaces. A method for reducing the dual integral equation to a hyper singular integral equation of second order is also proposed.