An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems
Ashyralyev A. Al-Hazaimeh H.
October 2023Multidisciplinary Digital Publishing Institute (MDPI)
Symmetry
2023#15Issue 10
This article is devoted to the study of the stability of time-dependent source identification telegraph type differential problems with dependent coefficients. Time-dependent source identification problems (SIPs) for telegraph differential equations (TDEs) with constant coefficients can be solved by classical integral-transform methods. However, these classical methods can be used, basically, in cases where the differential equation has constant coefficients. We establish the basic theorem of the stability of the time-dependent SIPs for the second-order linear differential equation (DE) in a Hilbert space with a self-adjoint positive definite operator (SAPDO) and damping term. In practice, stability estimates for the solution of the three types of SIPs for one-dimensional and for multidimensional TDEs with dependent coefficients and classic and non-classic conditions are obtained.
damping term , stability , TDE , time-dependent SIP
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Department of Mathematics, Bahcesehir University, Istanbul, 34353, Turkey
Department of Mathematics, Peoples Friendship University of Russia (RUDN University), Moscow, 117198, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Department of Mathematics, Faculty of Arts and Sciences, Near East University, TRNC, Mersin 10, Nicosia, 99138, Turkey
Department of Mathematics
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
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