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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 167, Pages 97–111 (Mi into491)  

Inverse linear problems for a certain class of degenerate fractional evolution equations

V. E. Fedorovabc, A. V. Nagumanovaa

a Chelyabinsk State University
b South Ural State University, Chelyabinsk
c Shadrinsk State Pedagogical University

Abstract: In this paper, we study the unique solvability of linear inverse coefficient problems with a time-independent unknown coefficient for evolution equations in Banach spaces with degenerate operators acting on the Gerasimov–Caputo fractional derivative. We apply abstract results obtained in the paper to the study of inverse problems with undetermined coefficients depending only on spatial variables for equations with polynomials on a self-adjoint, elliptic differential operator with respect to spatial variables. Also, we apply general results to the study of the unique solvability of inverse problems for time-fractional Sobolev systems.

Keywords: inverse coefficient problem, degenerate evolution equation, Gerasimov–Caputo fractional derivative

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.A03.21.0011
1.6462.2017/Ѕ„
This work was supported by the Government of the Russian Federation (Resolution of the Government No. 211, 16.03.2013, Agreement No. 02.A03.21.0011) and the Ministry of Education and Science of the Russian Federation (Government Task No. 1.6462.2017/BCh).


DOI: https://doi.org/10.36535/0233-6723-2019-167-97-111

Full text: PDF file (276 kB)
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UDC: 517.44; 517.9
MSC: 35R30, 35R11, 34K29

Citation: V. E. Fedorov, A. V. Nagumanova, “Inverse linear problems for a certain class of degenerate fractional evolution equations”, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22Ц26, 2018. Part III, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 167, VINITI, Moscow, 2019, 97–111

Citation in format AMSBIB
\Bibitem{FedNag19}
\by V.~E.~Fedorov, A.~V.~Nagumanova
\paper Inverse linear problems for a certain class of degenerate fractional evolution equations
\inbook Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22Ц26, 2018. Part III
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 167
\pages 97--111
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into491}
\crossref{https://doi.org/10.36535/0233-6723-2019-167-97-111}


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