Finding discontinuities in the coefficients of the linear nonstationary transport equations

Abstract

An X-ray tomography problem that is an inverse problem for the transport differential equation is set up and investigated. The absorption and single scattering of particles are taken into account. The transport equation is nonstationary (its coefficients and the unknown function depend on time), involves multiple energy levels, and its coefficients can undergo jump discontinuities with respect to the spatial variable (in other words, the medium in which the process proceeds is inhomogeneous). The sought object is the set on which the coefficients of the equation suffer a discontinuity, which corresponds to the search for the boundaries between the different substances composing the sensed medium.