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This article is cited in 2 scientific papers (total in 2 papers)
Mathematics
Linear inverse problems for degenerate evolution equations with the Gerasimov–Caputo derivative in the sectorial case
A. V. Nagumanovaa, V. E. Fedorovab a Chelyabinsk State University, 129 Kashirin Brothers Street, Chelyabinsk, Russia 454001
b South Ural State University (National Research University), 76 Lenin Avenue, Chelyabinsk, Russia 454080
Abstract:
We investigate the unique solvability of linear inverse problems for the evolution equation in a Banach space with a degenerate operator at the fractional Gerasimov–Caputo derivative and with a time-independent unknown coefficient. It is assumed that a pair of operators in the equation (at the unknown function and at its fractional derivative) generates a family of resolving operators of the corresponding degenerate linear homogeneous equation of the fractional order. The original problem is reduced to a system of two problems: the problem for an algebraic equation on the degeneration subspace of the original equation and the problem for the equation solved with respect to the fractional derivative, on the complement to the degeneration subspace. Two approaches are demonstrated. The first involves the study of the inverse problem for the equation solved with respect to the derivative and the direct problem for the algebraic equation. In the second approach, the inverse problem for the equation on the degeneration subspace is investigated firstly, then the direct problem for the second equation is researched. Abstract results are used to study initial-boundary value problems for a class of time-fractional order partial differential equations with an unknown coefficient depending on the spatial variables.
Keywords:
inverse coefficient problem, fractional Gerasimov–Caputo derivative, degenerate evolution equation, analytic in a sector resolving family of operators.
Received: 03.11.2019 Revised: 31.01.2020 Accepted: 30.04.2020
Citation:
A. V. Nagumanova, V. E. Fedorov, “Linear inverse problems for degenerate evolution equations with the Gerasimov–Caputo derivative in the sectorial case”, Mathematical notes of NEFU, 27:2 (2020), 54–76
Linking options:
https://www.mathnet.ru/eng/svfu285 https://www.mathnet.ru/eng/svfu/v27/i2/p54
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