On an inverse problem in the parabolic equation arising from groundwater pollution problem

In this paper, we consider an inverse problem to determine a source term in the parabolic equation, once the measured data are obtained at a later time. In general, this problem is ill-posed, therefore the Tikhonov regularization method with a priori and a posteriori parameter choice rule strategies is proposed to solve the problem. In the theoretical results, a priori error estimate between the exact solution and its regularized solution is obtained. For estimating the errors between the regularized solution and its exact solution, numerical experiments have been carried out. From the numerical results it shows that the a posteriori parameter choice rule method has a better convergence speed in comparison with the a priori parameter choice rule method.