Abstract
We consider a fractional diffusion equation with variable space-dependent order of the derivative in a bounded multidimensional domain. The initial data are homogeneous and the right-hand side and its time derivative satisfy some monotonicity conditions. Addressing the inverse problem with final overdetermination, we establish the uniqueness of a solution as well as some necessary and sufficient solvability conditions in terms of a certain constructive operator \( A \). Moreover, we give a simple sufficient solvability condition for the inverse problem. The arguments rely on the Birkhoff–Tarski theorem.
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 4, pp. 675–686. https://doi.org/10.33048/smzh.2023.64.402
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Artyushin, A.N. An Inverse Problem of Recovering the Variable Order of the Derivative in a Fractional Diffusion Equation. Sib Math J 64, 796–806 (2023). https://doi.org/10.1134/S003744662304002X
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DOI: https://doi.org/10.1134/S003744662304002X