Abstract
The space-dependent source identification problem for the two-dimensional neutron transport equation with spatially variable coefficients and periodic boundary conditions is investigated. The neutron transport equation is a fundamental model for neutron propagation in a medium, accounting for both streaming and collision events, and is critical for nuclear reactor safety analysis. While the source identification problem has been extensively studied for parabolic, elliptic, and hyperbolic equations, recent research has extended these methods to transport equations as well. The investigation begins with the homogeneous problem with constant coefficients, where an explicit solution is derived using the method of characteristics. This solution serves as the basis for studying the variable-coefficient case. A function is introduced to quantify the deviation of variable coefficients from constant values. Under suitable assumptions, a stability estimate is established, showing that the solution operator is exponentially bounded in time. Building on these results, this study investigates the inverse problem of identifying space-dependent source terms. By analyzing the equation structure and applying the stability estimate for the homogeneous problem, the study derives conditions for stable recovery of source terms from measured data. We introduce a time interval parameter and a contraction condition to make sure the solution is unique and depends continuously on the data. The main result provides stability estimates, showing that small changes in measured data lead to small changes in the identified sources. These theoretical contributions enhance the understanding of inverse problems for transport equations and have potential applications in reactor physics and related fields.