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In this paper, we consider an inverse problem to determine a source term in aparabolic equation, where the data are obtained at a certain time. In general,this problem is ill-posed, therefore the Tikhonov regularization method isproposed to solve the problem. In the theoretical results, a priori errorestimate between the exact solution and its regularized solutions is obtained.We also propose both methods, a priori and a posteriori parameter choice rules.In addition, the proposed methods have been verified by numerical experimentsto estimate the errors between the regularized solutions and exact solutions.Eventually, from the numerical results it shows that the a posteriori parameterchoice rule method gives a better the convergence speed in comparison with thea priori parameter choice rule method in some specific applications.

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