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In this paper we develop a time reversal method for the radiative transportequation to solve two problems: an inverse problem for the recovery of aninitial condition from boundary measurements, and the exact boundarycontrollability of the transport field with finite steering time. Absorbing andscattering effects, modeled by coefficients with low regularity, areincorporated in the formulation of these problems. This time reversal approachleads to a convergent iterative procedure to reconstruct the initial conditionprovided that the scattering coefficient is sufficiently small in the$L^{\infty}$ norm. Then, using duality arguments, we show that the solvabilityof the inverse problem leads to exact controllability of the transport fieldwith minimum-norm control obtained constructively. The solution approach toboth of these problems may have medical applications in areas such as opticalimaging and optimization of radiation delivery for cancer therapy.

Time reversal for radiative transport with applications to inverse and control problems