INVERSE SOURCE RECOVERY IN A CLASS OF SINGULAR DIFFUSION EQUATIONS VIA OPTIMAL CONTROL
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Date
2025
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Abstract
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 Tikhonovregularized
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.