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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 57

Обратная задача определения ядра в уравнении Мура – Гибсона – Томпсона

Author(s)

Durdimurod K. Durdiev1, Askar A. Rahmonov1,3, Asliddin A. Boltaev2

1 Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan 

2 Bukhara State University, Bukhara, Uzbekistan 

3 Samarkand State University, Samarkand, Uzbekistan

Abstract
We investigate an inverse problem of determining the kernel function 𝑔(𝑡) in the third-order Moore–Gibson–Thompson (MGT) equation. First, the solution to the direct initial–boundary value problem for a homogeneous MGT equation is constructed using the Fourier spectral method. Then, based on this solution and the overdetermination condition, a Volterra-type integral equation is derived to study the inverse problem. We prove global existence and uniqueness results for the solutions of the considered problems. In addition, stability estimates for the solution of the direct and inverse problem are obtained.
About the Authors

Durdimurod K. Durdiev, Dr. Sci. (Phys.–Math.), Prof., Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan, Tashkent, 100170, Uzbekistan, d.durdiyev@mathinst.uz 

Askar A. Rahmonov, Dr. Sci. (Phys.–Math.), Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan, Tashkent, 100170, Uzbekistan; Samarkand State University, Samarkand, 140104, Uzbekistan, araxmonov@mail.ru 

Asliddin A. Boltaev, Dr. of philosophy(PhD) in phys. and math. sciences, Bukhara State University, Bukhara, 705018, Uzbeksitan, asliddinboltayev@mail.ru 

For citation
Durdiev D. K., Rahmonov A. A., Boltaev A. A. Kernel Determination Inverse Problem in the Moore–Gibson–Thompson Equation. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 57, pp. 48–65. https://doi.org/10.26516/1997-7670.2026.57.48
Keywords
MGT equation, initial-boundary value problem, integral equation, inverse problem, Banach principle
UDC
517.968
MSC
35A01, 35A09, 35G16, 45D05
DOI
https://doi.org/10.26516/1997-7670.2026.57.48
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