An inverse problem of finding the time-dependent thermal conductivity from boundary data

Huntul, M. J.; Lesnic, D.

doi:10.1016/j.icheatmasstransfer.2017.05.009

Cited by 36 publications

(11 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

Huntul¹,

Oussaeif²

2022

Computer Systems Science and Engineering

View full text Add to dashboard Cite

show abstract

“…Kwon considered the anisotropic inverse conductivity and scattering problems [14]. The inverse problem of time-dependent thermal conductivity was studied by Huntul and Lesnic by recasting the original problems into the nonlinear least-squares minimization [15]. Isakov and Sever provided an integral equation method for inverse conductivity problems using the linearization method [16].…”

Section: Introductionmentioning

confidence: 99%

Solving Inverse Conductivity Problems in Doubly Connected Domains by the Homogenization Functions of Two Parameters

et al. 2022

View full text Add to dashboard Cite

In the paper, we make the first attempt to derive a family of two-parameter homogenization functions in the doubly connected domain, which is then applied as the bases of trial solutions for the inverse conductivity problems. The expansion coefficients are obtained by imposing an extra boundary condition on the inner boundary, which results in a linear system for the interpolation of the solution in a weighted Sobolev space. Then, we retrieve the spatial- or temperature-dependent conductivity function by solving a linear system, which is obtained from the collocation method applied to the nonlinear elliptic equation after inserting the solution. Although the required data are quite economical, very accurate solutions of the space-dependent and temperature-dependent conductivity functions, the Robin coefficient function and also the source function are available. It is significant that the nonlinear inverse problems can be solved directly without iterations and solving nonlinear equations. The proposed method can achieve accurate results with high efficiency even for large noise being imposed on the input data.

show abstract

“…Bollati, Briozzo and Natale successfully discussed about inverse non-classical Stefan problem in which unknown thermal coefficients have to be determined [25] and Briozzo, Natale with Tarzia considered inverse non-classical Stefan problem for Storm's-type materials through a phase-change process [26]. Huntul and Lesnic also discussed an inverse problem of determining the time-dependent thermal conductivity and the transient temperature satisfying the heat equation with boundary data [27].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Stefan Problem for one-phase generalized heat equation with heat flux and convective boundary condition

Nauryz¹

2022

Preprint

View full text Add to dashboard Cite

In this article we consider a mathematical model of an initial stage of closure electrical contact that involves a metallic vaporization after instantaneous exploding of contact due to arc ignition with power P 0 on fixed face z = 0 and heat transfer in material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component with heat flux and convective boundary conditions prescribed at the known free boundary z = α(t). The temperature field in the liquid region of such kind of material can be modelled by Stefan problem for the generalized heat equation. The method of solution is based on similarity variable, which enables us to reduce generalized heat equation to nonlinear ordinary differential equation. Moreover, we have to determine temperature solution for the liquid phase and location of melting interface. Existence and uniqueness of the solution is proved by using the fixed point Banach theorem. The solution for two cases of thermal coefficients, in particular, constant and linear thermal conductivity are represented, existence and uniqueness for each type of solution is proved.

show abstract

An inverse problem of finding the time-dependent thermal conductivity from boundary data

Cited by 36 publications

References 8 publications

Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

Solving Inverse Conductivity Problems in Doubly Connected Domains by the Homogenization Functions of Two Parameters

Nonlinear Stefan Problem for one-phase generalized heat equation with heat flux and convective boundary condition

Contact Info

Product

Resources

About