Direct and inverse problems for diffusion operator with discontinuity points

Abstract

In this study, the diffusion operator with discontinuity points has been considered. Under certain initial and jump conditions, integral equations have been derived for solutions and integral representation have been presented. Some important spectral properties of eigenvalue and eigenfunctions have been obtained. Reconstruction of the diffusion operator with discontinuity points problem have been proved by Weyl function, spectral datas and two sectra.