M.J. Huntul^*

Computer Systems Science and Engineering, Vol.39, No.3, pp. 415-429, 2021, DOI:10.32604/csse.2021.017924

Abstract The aim of this paper is to find the time-dependent term numerically in a two-dimensional heat equation using initial and Neumann boundary conditions and nonlocal integrals as over-determination conditions. This is a very interesting and challenging nonlinear inverse coefficient problem with important applications in various fields ranging from radioactive decay, melting or cooling processes, electronic chips, acoustics and geophysics to medicine. Unique solvability theorems of these inverse problems are supplied. However, since the problems are still ill-posed (a small modification in the input data can lead to bigger impact on the ultimate result in the output solution) the solution needs… More >

M. J. Huntul^*

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 3681-3699, 2021, DOI:10.32604/cmc.2021.016036

Abstract The inverse problem of reconstructing the time-dependent thermal conductivity and free boundary coefficients along with the temperature in a two-dimensional parabolic equation with initial and boundary conditions and additional measurements is, for the first time, numerically investigated. This inverse problem appears extensively in the modelling of various phenomena in engineering and physics. For instance, steel annealing, vacuum-arc welding, fusion welding, continuous casting, metallurgy, aircraft, oil and gas production during drilling and operation of wells. From literature we already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the… More >