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Uniqueness for an Inverse Source Problem of Determining a Space-Dependent Source in a Non-Autonomous Time-Fractional Diffusion Equation

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Abstract

We study uniqueness of a solution for an inverse source problem arising in linear time-fractional diffusion equations with time-dependent coefficients. We consider source term in a separated form h(t)f(x). The unknown source f(x) is recovered from the final time measurement u(x, T). A new uniqueness result is formulated in Theorem 3.1 under the assumption that h ∈ C([0, T]) and 0 ≡ h ≥ 0. No monotonicity in time for h(t) and for coefficients of the differential operator is required.

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  1. Research Group Numerical Analysis and Mathematical Modelling Department of Electronics and Information Systems, Ghent University, Krijgslaan 281, 9000, Ghent, Belgium

    Marian Slodička

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  1. Marian Slodička
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Correspondence to Marian Slodička.

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Slodička, M. Uniqueness for an Inverse Source Problem of Determining a Space-Dependent Source in a Non-Autonomous Time-Fractional Diffusion Equation. Fract Calc Appl Anal 23, 1702–1711 (2020). https://doi.org/10.1515/fca-2020-0084

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  • DOI: https://doi.org/10.1515/fca-2020-0084

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