Abstract

The authors consider the problem of finding a two-dimensional heat source having the form \(\phi(t)f(x,t)\) in a heat conduction body \(Q\). Assuming \(\partial Q\) is insulated and \(\phi\neq 0\), the authors show that the heat source is defined uniquely by the temperature history on \(\partial Q\) and the temperature distribution in \(Q\) at the initial time \(t=0\) and the final time \(t=1\). Using the method of truncated integration and the Fourier transform, the authors construct regularization solutions and derive explicitly an error estimate.