Determination of forcing functions in the wave equation. Part II: the time-dependent case

An unknown time-dependent force function in the wave equation is investigated in this study. This is a natural continuation of Part I [J Eng Math 2015, this volume], where the space-dependent force identification has been considered. Additional data are given by a space integral average measurement of the displacement. This linear inverse problem has a unique solution, but it is still ill-posed since small errors in the input data cause large errors in the output solution. Consequently, when the input data are contaminated with noise, we use the Tikhonov regularization method in order to obtain a stable solution. The choice of the regularization parameter is based on the L-curve method. Numerical results show that the solution is accurate for exact data and stable for noisy data.