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On the uniqueness of the inverse source problem for linear particle transport theory. (English) Zbl 1156.82391

Summary: Inverse source problems for time-independent linear transport with data from invasive and noninvasive detectors are analyzed. The former inverse problem is proven to have a unique solution, while for the latter we construct counterexamples that prove that the problem is underdetermined for the general case of anisotropic sources and prove that it has a unique solution for isotropic sources and scattering. Using duality we propose and analyze a general class of inverse source algorithms. The emphasis is on establishing new inversion techniques and in proving uniqueness or nonuniqueness as well as to find, when possible, ways to regularize the inverse source problem.

MSC:

82C70 Transport processes in time-dependent statistical mechanics
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
65R10 Numerical methods for integral transforms

Software:

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