Identifying an unknown source term in a heat equation with time-dependent coefficients

An inverse source problem for an n-dimensional heat equation with a time-varying coefficient is investigated. The spatially dependent component of a source function is determined from a measurement at the final time. The inverse problem is regularized by a mollification method. Hölder-type stability estimates are proved. Error estimates of Hölder type are also proved for regularized solutions for both a priori and a posteriori mollification parameter choice rules. A non-iterative reconstruction algorithm is proposed. Numerical examples in one and two dimensions are shown to illustrate the performance of the proposed method.