Inverse coefficient problem for differential equation in partial derivatives of a fourth order in time with integral over-determination

Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity. The inverse problems for higher order derivatives in time equations connected with recovery of the coefficient are scarce and need additional cons...

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Bibliographic Details
Main Authors: M.J. Huntul, I. Tekin
Format: Article
Language:English
Published: Academician Ye.A. Buketov Karaganda University 2022-12-01
Series:Қарағанды университетінің хабаршысы. Математика сериясы
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Online Access:http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/526
Description
Summary:Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity. The inverse problems for higher order derivatives in time equations connected with recovery of the coefficient are scarce and need additional consideration. In this article the inverse problem of determination is considered, which depends on time, lowest term coefficient in differential equation in partial derivatives of fourth order in time with initial and boundary conditions from an additional integral observation. Under some conditions of regularity, consistency and orthogonality of data by using of the contraction principle the unique solvability of the solution of the coefficient identification problem on a sufficiently small time interval has been proved.
ISSN:2518-7929
2663-5011