An inverse time-dependent source problem for the heat equation

In this paper the inverse problem of finding the time-dependent heat source together with the temperature solution of heat equation with nonlocal boundary and integral additional conditions is investigated. The existence, uniqueness and continuous dependence of the solution of the inverse problem upon the data are established. Furthermore, a boundary element method combined with the Tikhonov regularization of various orders is developed in order to obtain a stable solution. Numerical results are presented and discussed.