Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation
https://doi.org/10.26907/0021-3446-2023-12-3-16
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.
About the Authors
D. K. Durdiev
Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan; Bukhara State University
Uzbekistan
Uzbekistan
Durdimurod Kalandarovich Durdiev
46 University str., Tashkent, 100170; 11 Muhammad Ikbal str., Bukhara, 200118
A. A. Boltaev
Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan; Bukhara State University
Uzbekistan
Uzbekistan
Asliddin Askar ugli Boltaev
46 University str., Tashkent, 100170; 11 Muhammad Ikbal str., Bukhara, 200118
A. A. Rahmonov
Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan; Bukhara State University
Uzbekistan
Uzbekistan
Askar Ahmadovich Rahmonov
46 University str., Tashkent, 100170; 11 Muhammad Ikbal str., Bukhara, 200118
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Review
For citations:
Durdiev D.K., Boltaev A.A., Rahmonov A.A. Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2023;1(12):3-16. (In Russ.) https://doi.org/10.26907/0021-3446-2023-12-3-16
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