Determination of a spacewise-dependent heat source by a logarithmic-type regularization method

Abstract

This paper is devoted to an inverse problem of determining a spacewise-dependent heat source in a linear parabolic equation from the measurement at the final moment. A new regularization method called the logarithmic-type regularization method is proposed to determine the unknown source. Then the convergence estimates of regularization solutions are obtained under the a-priori and a-posteriori regularization parameter selections. Finally, some numerical examples are presented to verify the validity of the logarithmic-type regularization method.