Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data

This paper addresses an inverse source problem for a linearized Boltzmannequation, a model that arises in important applications such as rarefied gas dynamics,radiative transfer, and particle transport. The aim is to determine an unknown source termfrom the model equation together with appropriate observational data. Under structuralconvexity assumptions on the Hamiltonian and an L2-boundedness condition on the linearizedcollision operator, uniqueness for the inverse source problem is proved using boundary traceand gradient data. The proof relies on a pointwise energy identity for the transport operatorcombined with estimates for the collision contribution.