Increasing regularity of generalized solutions to the wave equation for computing optimal boundary controls

D. A. Ivanov

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: Problems with two-sided boundary controls of three main types are considered for the wave equation in the classes of weak generalized solutions on intervals of subcritical length. An algorithm is proposed for the stable approximation of boundary controls. This algorithm is based on the preliminary smoothing of phase trajectories, the application of a variational method in the classes of strong generalized solutions, and the final differentiation of the resulting smoothed controls. Numerical results are discussed.

Keywords: wave equation, generalized solution, boundary control, subcritical interval, approximate data, approximate solution, convergence.

UDC: 517.956.37

Received: 01.07.2016