INVERSE SOURCE RECOVERY IN A CLASS OF SINGULAR DIFFUSION EQUATIONS VIA OPTIMAL CONTROL (Journal of Mathematics Mechanics and Computer Science, 2025)
This paper addresses the inverse problem of identifying a space-dependent source term in a singular parabolic equation involving an inverse-square potential, knowing final time measurement data. The problem is reformulated within an optimal control framework, minimizing a   Tikhonov regularized functional to ensure stability. Theoretical contributions include existence and uniqueness of weak solutions for the direct problem, along with a stability estimate for the inverse problem under a first-order optimality condition. A Landweber-type iterative algorithm is designed for numerical reconstruction, validated through synthetic examples with both exact and noisy data
Keywords: Inverse problem; singular parabolic equation; stability; regularization; Landweber method