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

Let Q be a heat conduction body and let phi = phi(t) be given. We consider the problem of finding a two-dimensional heat source having the form phi(t) f (x, y) in Q. The problem is ill-posed. Assuming partial derivative Q is insulated and phi not equivalent to 0, we show that the heat source is defined uniquely by the temperature history on partial derivative Q and the temperature distribution in Q at the initial time t = 0 and at the final time t = 1. Using the method of truncated integration and the Fourier transform, we construct regularized solutions and derive explicitly error estimate. (c) 2005 Elsevier B.V. All rights reserved.