Identifying an unknown source term in a spherically symmetric parabolic equation

The aim of this work is to solve the inverse problem of determining an unknown source term in a spherically symmetric parabolic equation. The problem is ill-posed: the solution (if it exists) does not depend continuously on the final data. A spectral method is applied to formulate a regularized solution, and a Hِlder type estimate of the error between the approximate solution and the exact solution is obtained with a suitable choice of regularization parameter.