Determination of the source function in a parabolic equation (Q1921566)

The author considers the problem of determination of the unknown time component of the source term in a parabolic partial differential equation. With certian restrictions, an approximation of the problem, based on the finite-element method, is constructed. Using a combination of Krasovskij's principle of extremal aiming and Tikhonov's regularization method, a finite-step algorithm for determining the unknown function is presented. The algorithm is stable to information noise and computation errors, and it operates in real time by a feedback scheme. The algorithm uses information at finite time nodes. The question of convergence is also discussed.