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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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Published/Copyright: December 31, 2020

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 hC ([0, T]) and 0 ≢ h ≥ 0. No monotonicity in time for h(t) and for coefficients of the differential operator is required.


Editorial Note

This paper has been presented at the online international conference “WFC 2020: Workshop on Fractional Calculus”, Ghent University, Belgium, 9–10 June 2020.


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Received: 2020-06-10
Published Online: 2020-12-31
Published in Print: 2020-12-16

© 2020 Diogenes Co., Sofia

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