Determination of Spacewise− Dependent Heat Source Term in Pseudoparabolic Equation from Overdetermination Conditions

Abstract

      This paper examines the finding of spacewise dependent heat source function in pseudoparabolic equation with initial and homogeneous Dirichlet boundary conditions, as well as the final time value / integral specification as additional conditions that ensure the uniqueness solvability of the inverse problem. However, the problem remains ill-posed because tiny perturbations in input data cause huge errors in outputs. Thus, we employ Tikhonov’s regularization method to restore this instability. In order to choose the best regularization parameter, we employ L-curve method. On the other hand, the direct (forward) problem is solved by a finite difference scheme while the inverse one is reformulated as an optimization problem. The later problem is accomplished by employing lsqnolin subroutine from MATLAB. Two test examples are presented to show the efficiency and accuracy of the employed method by including many noises level and various regularization parameters.