Inverse source problem for a time-fractional heat equation with generalized impedance boundary condition

2016/07/12 by M. Cicek, Cicek, M., Mansur I. Ismailov +2
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1607.03311

openalex publication_date 2016/07/12 · arxiv created 2016/09/05 · arxiv updated 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper considers an inverse source problem for a one-dimensional time-fractional heat equation with the generalized impedance boundary condition. The inverse problem is the time dependent source parameter identification together with the temperature distrubution from the energy measurement. The well-posedness of the inverse problem is shown by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition and by using the results on Volterra type integral equation with the kernel may have a diagonal singularity.

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