Inverse Boundary-Value Problem for Linearized Equation of Motion of a Homogeneous Elastic Beam

Abbasova, Khatira E.; Mehraliyev, Yashar T.; Azizbayov, Elvin I.

doi:10.12732/ijam.v33i1.12

Cited by 2 publications

(3 citation statements)

References 5 publications

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“…be a rectangle domain. Consider the following inverse problem of determining a pair of functions (u(x, t), p(t)), [1]…”

Section: The Formultion Of the Problemmentioning

confidence: 99%

“…In this study, a one-dimensional hyperbolic inverse problem was presented of the second-order to investigate the retrieval of timewise potential term numerically from the additional measurement, with initial conditions and non-local integral condition. The uniqueness and existence already proved by Yashar in [1], but no numerical investigation has been carried out till now.…”

Section: Introductionmentioning

confidence: 99%

“…The author in [22] studied the hyperbolic heat conduction inverse problem to reconstruct the unknown surface heat flux from the temperature measurements. While, in [1] presented the classical solution for the linearized equation of motion of a homogeneous elastic beam which is hyperbolic fourth order problem with periodic conditions.…”

Section: Introductionmentioning

confidence: 99%

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Numerical identification of timewise dependent coefficient in Hyperbolic inverse problem

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Advances in the Theory of Nonlinear Analysis and Its Application

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This article investigates the nonlocal inverse initial boundary-value problem in a rectangular domain, hyperbolic second order inverse problem. The main objective is to find the unidentified coefficient and offer a solution to the problem. The hyperbolic second-order, nonlinear equation is solved using finite difference method (FDM). However, the inverse problem was successfully solved by the MATLAB subroutine lsqnonlin from the optimization toolbox after being reformulated as a nonlinear regularized least-square op-timization problem with a simple bound on the unknown quantity. Given that the studied problem is often ill-posed and that even a minor error in the input data can have a large impact on the output. Tikhonov's regularization technique is used to generate stable and accurate results.

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“…be a rectangle domain. Consider the following inverse problem of determining a pair of functions (u(x, t), p(t)), [1]…”

Section: The Formultion Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical identification of timewise dependent coefficient in Hyperbolic inverse problem

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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Determination of a Coefficient and Kernel in a Two-dimensional Fractional Integrodifferential Equation

Rahmonov,

Akramova,

Elmuradova

et al. 2024

Lobachevskii J Math

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Inverse Boundary-Value Problem for Linearized Equation of Motion of a Homogeneous Elastic Beam

Cited by 2 publications

References 5 publications

Numerical identification of timewise dependent coefficient in Hyperbolic inverse problem

Numerical identification of timewise dependent coefficient in Hyperbolic inverse problem

Determination of a Coefficient and Kernel in a Two-dimensional Fractional Integrodifferential Equation

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