Finding the unknown boundary in the initial boundary-value problem for the heat equation

The article considers the determination of the boundary of a two-dimensional region in which an initial boundary-value problem for the heat equation is defined, given the solution of the problem for all time instants at some points of the region. The direct problem is reduced to an integral equation, and numerical solutions of the inverse problem are obtained for the case when the boundary is an ellipse. We investigate the sensitivity of the observed variables to the location (relative to the boundary) of the point where the right-hand side of the equation is specified. Translated from Prikladnaya Matematika i Informatika, No. 30, 2008, pp. 18–24.