Reconstruction of the Discontinuity Line of a Piecewise-Constant Coefficient in the Two-Dimensional Internal Initial–Boundary Value Problem for the Homogeneous Heat Equation

We investigate the reconstruction of the discontinuity line of a piecewise-constant coefficient in the two-dimension internal initial–boundary value problem for the one-dimensional heat equation. Supplementary data include the direct problem solution, which is known for finitely many boundary points at all times. The results of computer experiments reported in the article show that the inverse problem is well-conditioned in this setting. The direct problem has been reduced to the boundary-value problem for the Helmholtz equation and its solution was expressed in terms of potentials.