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Inverse Problem for the Fractional Diffusion Equation in Schwarz-Type Spaces

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We establish sufficient conditions for the unique solvability of the inverse problem of finding two unknown functions from a Schwarz-type space of smooth functions rapidly decreasing at infinity on the right-hand side of the diffusion equation with Caputo–Djrbashian time fractional derivative. In this case, we use two overdetermination conditions integral with respect to time.

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Authors and Affiliations

  1. Rzeszów University, Rzeszów, Poland

    А. О. Lopushansky

  2. I. Franko National University of Lviv, Lviv, Ukraine

    H. P. Lopushanska

Authors
  1. А. О. Lopushansky
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  2. H. P. Lopushanska
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Correspondence to H. P. Lopushanska.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 4, pp. 49–59, October–December, 2019.

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Lopushansky, А.О., Lopushanska, H.P. Inverse Problem for the Fractional Diffusion Equation in Schwarz-Type Spaces. J Math Sci 265, 394–407 (2022). https://doi.org/10.1007/s10958-022-06060-y

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