INVERSE SOURCE RECOVERY IN A CLASS OF SINGULAR DIFFUSION EQUATIONS VIA OPTIMAL CONTROL

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DOI:

https://doi.org/10.26577/JMMCS202512739
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Keywords:

Inverse problem, singular parabolic equation, stability, regularization, Landweber method

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   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

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How to Cite

Nedjma, M., & Chattouh, A. . (2025). INVERSE SOURCE RECOVERY IN A CLASS OF SINGULAR DIFFUSION EQUATIONS VIA OPTIMAL CONTROL. Journal of Mathematics, Mechanics and Computer Science, 127(3). https://doi.org/10.26577/JMMCS202512739