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.
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).
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 22–26, 2018. Part III, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 167, VINITI, Moscow, 2019, 97–111
\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 22–26, 2018. Part III
\serial Itogi Nauki i Tekhniki. 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}
Linking options:
https://www.mathnet.ru/eng/into491
https://www.mathnet.ru/eng/into/v167/p97
This publication is cited in the following 5 articles:
A. A. Matchanova, B. J. Kadirkulov, T. K. Yuldashev, “Mixed Problem for a Linear Barenblatt–Zheltov–Kochina Equation with Fractional Hilfer Operator”, Lobachevskii J Math, 45:7 (2024), 3333
R. R. Ashurov, Yu. E. Fayziev, N. Kh. Khushvaktov, “Non-Local Problem in Time for the Barenblatt–Zheltov–Kochina Type Fractional Equations”, Lobachevskii J Math, 44:12 (2023), 5164
M. V. Plekhanova, A. F. Shuklina, “Smeshannoe upravlenie dlya polulineinykh uravnenii drobnogo poryadka”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 212, VINITI RAN, M., 2022, 64–72
M. V. Plekhanova, E. M. Izhberdeeva, “O korrektnosti obratnoi zadachi dlya vyrozhdennogo evolyutsionnogo uravneniya s drobnoi proizvodnoi Dzhrbashyana—Nersesyana”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 213, VINITI RAN, M., 2022, 80–88
V. E. Fedorov, M. Kostić, “Identification Problem for Strongly Degenerate Evolution Equations with the Gerasimov–Caputo Derivative”, Diff Equat, 56:12 (2020), 1613
Citation in format AMSBIB
Contact us: