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Convolution Kernel Determination Problem in the Third Order Moore–Gibson–Thompson Equation

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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.

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Funding

The work of A.A. Boltaev was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-02-2023-914.

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Authors and Affiliations

  1. Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan, 100170, Tashkent, Republic of Uzbekistan

    D. K. Durdiev, A. A. Boltaev & A. A. Rahmonov

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  1. D. K. Durdiev
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  2. A. A. Boltaev
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  3. A. A. Rahmonov
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Correspondence to D. K. Durdiev, A. A. Boltaev or A. A. Rahmonov.

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Durdiev, D.K., Boltaev, A.A. & Rahmonov, A.A. Convolution Kernel Determination Problem in the Third Order Moore–Gibson–Thompson Equation. Russ Math. 67, 1–13 (2023). https://doi.org/10.3103/S1066369X23120034

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