Abstract

Authors investigated the two-dimensional heat transfer problem on the space domain where \(x \in \Re\) and \( y \in (1,2)\). The unknown function is the heat flux on the line \((x,1)\) with given zero initial condition and prescribed boundary conditions on lines \((x,1)\) and \((x,2)\) for all positive time \(t>0\). Considering this problem on the global time interval it is ill-posed. Authors present some regularization of the problem via transferring it to the convolution equation. Then using the method of truncated integration, the Fourier transform of the solution can be approximated by function having the compact support in \(\Re^2\). The solution is then represented by an expansion of two-dimensional Sinc series. The error estimates for this approximation are derived and proved. Numerical examples with an exact solution for comparison with this regularized representation are included.