Determination of a two-dimensional heat source: Uniqueness, regularization and error estimate

摘要

Let be a heat conduction body and let be given. We consider the problem of finding a two-dimensional heat source having the form in . The problem is ill-posed. Assuming is insulated and , we show that the heat source is defined uniquely by the temperature history on and the temperature distribution in at the initial time and at the final time . Using the method of truncated integration and the Fourier transform, we construct regularized solutions and derive explicitly error estimate.