Abstract:
This article is concerned with the study of the inverse problem of determining the difference kernel in a Volterra type integral term function in the third-order Moore–Gibson–Thompson (MGT) equation. First, the initial-boundary value problem is reduced to an equivalent problem. Using the Fourier spectral method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution to the integral equations are proved. The obtained solution to the integral equations of Volterra-type is also the unique solution to the equivalent problem. Based on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original inverse problem is proved.
Keywords:
MGT equation, initial-boundary value problem, inverse problem, existence, uniqueness.
Citation:
D. K. Durdiev, A. A. Boltaev, A. A. Rahmonov, “Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 12, 3–16
\Bibitem{DurBolRak23}
\by D.~K.~Durdiev, A.~A.~Boltaev, A.~A.~Rahmonov
\paper Convolution kernel determination problem in the third order Moore--Gibson--Thompson equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 12
\pages 3--16
\mathnet{http://mi.mathnet.ru/ivm9922}
\crossref{https://doi.org/10.26907/0021-3446-2023-12-3-16}
Linking options:
https://www.mathnet.ru/eng/ivm9922
https://www.mathnet.ru/eng/ivm/y2023/i12/p3
This publication is cited in the following 1 articles:
U. D. Durdiev, A. A. Rakhmonov, “Obratnaya zadacha dlya differentsialnogo uravneniya chetvertogo poryadka s drobnym operatorom Kaputo”, Izv. vuzov. Matem., 2024, no. 9, 22–33
Citation in format AMSBIB
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