<p>We investigate the inverse problem of identifying a space-depen- dent potential in a Caputo time-fractional diffusion equation from boundary observations. Our analysis establishes a maximum principle for subdiffusion equations with non-homogeneous Neumann boundary conditions, demonstrating the positivity of solutions under specific assumptions on the boundary data. Building upon this result, we leverage the Gâteaux differentiability of the forward map and the non-vanishing property of its derivative to derive a local Lipschitz stability estimate for the inverse potential problem. This provides a rigorous foundation for the stable reconstruction of the potential, highlighting the interplay between fractional dynamics and stability in inverse problems.</p>

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Stability estimate for an inverse potential problem in time-fractional diffusion problem

  • Hamza Kahlaoui

摘要

We investigate the inverse problem of identifying a space-depen- dent potential in a Caputo time-fractional diffusion equation from boundary observations. Our analysis establishes a maximum principle for subdiffusion equations with non-homogeneous Neumann boundary conditions, demonstrating the positivity of solutions under specific assumptions on the boundary data. Building upon this result, we leverage the Gâteaux differentiability of the forward map and the non-vanishing property of its derivative to derive a local Lipschitz stability estimate for the inverse potential problem. This provides a rigorous foundation for the stable reconstruction of the potential, highlighting the interplay between fractional dynamics and stability in inverse problems.