Coefficient determination for the stationary anisotropic Boltzmann transport equation

The problem of simultaneous spatial determination of the absorption and scattering coeficients in the stationary linear one velocity Boltzmann transport equation via boundary measurements is investigated. The original first-order problem is shown to be equivalent to a second order self-adjoint problem. Then, I introduce an a priori operator K that can be different from the scattering but gives compactness to the problem. The associated eigenvalue problem generates a dense and complete set of eigenfunctions in the Hilbert space where the problem is defined. It is shown that the traces of eigenfunctions form a minimal system in the trace boundary space and that appropriate boundary values may be chosen in order to establish a bi-orthogonal set. The identifiability for the extinction and scattering coefficients is suggested. Numerical experiments with the original first order problem are presented.