Browsing by Author "Mahdi, Nedjma"

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    INVERSE SOURCE RECOVERY IN A CLASS OF SINGULAR DIFFUSION EQUATIONS VIA OPTIMAL CONTROL
    (2025) Mahdi, Nedjma
    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.