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Specific Cases of One General Inverse Problem for Abstract Differential Equations

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Abstract

We consider a general statement of linear inverse problem for \(n\)-th order abstract differential equation in a Banach space. A universal uniqueness criterion for a solution of this problem is given. It is expressed through zeros of special Mittag-Leffler functions. The main emphasis is placed on the cases when all zeros of the functions are found explicitly and the uniqueness criterion takes an elementary form. It is shown that the previous results for equations of the \(1\)st and \(2\)nd orders follow from the general criterion. Fundamentally new is the case of one inverse problem for the \(4\)th order differential equation, where the result also takes an elementary form. This last case is discussed in detail in our paper.

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ACKNOWLEDGMENTS

We thank V.E. Fedorov and V.B. Sherstyukov for supporting our paper.

Funding

The work was prepared also with the financial support of the Ministry of Education and Science of Russia as part of the implementation of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement no. 075-15-2022-284.

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Authors and Affiliations

  1. Lomonosov Moscow State University, 119991, Moscow, Russia

    M. Almohamed & I. V. Tikhonov

  2. Moscow Technical University of Communications and Informatics, 123423, Moscow, Russia

    M. Almohamed

  3. Moscow State Pedagogical University, 107140, Moscow, Russia

    I. V. Tikhonov

Authors
  1. M. Almohamed
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  2. I. V. Tikhonov
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Correspondence to M. Almohamed or I. V. Tikhonov.

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(Submitted by T. K. Yuldashev)

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Almohamed, M., Tikhonov, I.V. Specific Cases of One General Inverse Problem for Abstract Differential Equations. Lobachevskii J Math 44, 502–509 (2023). https://doi.org/10.1134/S1995080223020063

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  • DOI: https://doi.org/10.1134/S1995080223020063

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