Reconstructing the Time-Dependent Thermal Coefficient in 2D Free Boundary Problems

Huntul, M. J.

doi:10.32604/cmc.2021.016036

Cited by 6 publications

(1 citation statement)

References 20 publications

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“…For instance, for heat propagation in a thin rod in which the law of variation θ(t) of the total quantit of heat in the rod is given in [18]. In addition, the inverse problem of determining the time-dependent coefficient in a one and twodimensional parabolic equation from nonlocal integral over-specification condition has been investigated widely by many researchers in the past, see [19][20][21][22][23] to mention only a few.…”

Section: Introductionmentioning

confidence: 99%

Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

Huntul¹,

Oussaeif²

2022

Computer Systems Science and Engineering

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In this paper, we consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation whose leading coefficient depends on time variable under nonlocal integral overdetermination condition. We obtain sufficient conditions for the unique solvability of the inverse problem. The existence and uniqueness of the solution of the inverse parabolic problem upon the data are established using the fixed point theorem. This inverse problem appears extensively in the modelling of various phenomena in engineering and physics. For example, seismology, medicine, fusion welding, continuous casting, metallurgy, aircraft, oil and gas production during drilling and operation of wells. In addition, the numerical solution of the inverse problem is studied by using the Crank-Nicolson finite difference method together with the Tikhonov regularization to find a stable and accurate approximate solution of finite differences. The resulting nonlinear system of parabolic equation is solved computationally using the MATLAB subroutine lsqnonlin. Both analytical and numerically simulated noisy input data are inverted. The root mean square error values for various noise levels for both continuous and discontinuous time-dependent heat source term are compared. Numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data. Furthermore, the choice of the regularization parameter is also discussed based on the trial and error technique.

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Section: Introductionmentioning

confidence: 99%

Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

Huntul¹,

Oussaeif²

2022

Computer Systems Science and Engineering

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On the solvability of an inverse boundary problem for the equation of transverse oscillation of the rod

Huntul,

Ramazanova,

Mehraliyev

2024

Math Methods in App Sciences

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In this article, the solvability of an inverse boundary problem for the 2D equation of transverse oscillation of the rod from knowledge of additional condition is studied. To investigate the solvability of the inverse problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence to the original problem in a certain sense. Using the contraction mappings principle existence and uniqueness of the solution of an equivalent problem is proved. Further, using the equivalency, the existence and uniqueness theorems of the classical solution of the original problem are proved.

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Identification of the unknown heat source terms in a 2D parabolic equation

Huntul

2021

Journal of King Saud University - Science

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Reconstructing the Time-Dependent Thermal Coefficient in 2D Free Boundary Problems

Cited by 6 publications

References 20 publications

Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

On the solvability of an inverse boundary problem for the equation of transverse oscillation of the rod

Identification of the unknown heat source terms in a 2D parabolic equation

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