Reconstructing The Moore-Gibson-Thompson Equation

Al‐Khulaifi, Waled; Boumenir, Amin

doi:10.1515/msds-2020-0117

Nonautonomous Dynamical Systems

2020

DOI: 10.1515/msds-2020-0117

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Reconstructing The Moore-Gibson-Thompson Equation

Waled Al‐Khulaifi

Amin Boumenir

Abstract: We are concerned with the inverse problem of recovering a third order Moore-Gibson-Thompson equation from a single observation of its solution at an arbitrary point. We show how to reconstruct its three unknown parameters and the memory kernel by using the Laplace transform.

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Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation

Durdiev,

Boltaev,

Rahmonov

2023

jour

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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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Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation

Durdiev,

Boltaev,

Rahmonov

2023

jour

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

Durdiev,

Boltaev,

Rahmonov

2023

Russ Math.

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Reconstructing The Moore-Gibson-Thompson Equation

Abstract: We are concerned with the inverse problem of recovering a third order Moore-Gibson-Thompson equation from a single observation of its solution at an arbitrary point. We show how to reconstruct its three unknown parameters and the memory kernel by using the Laplace transform.

Cited by 2 publications

References 12 publications

Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation

Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation

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

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