Simultaneous identification of the initial data in a degenerate and singular hyperbolic wave equation
摘要
This paper is devoted to the determination of the initial data in a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. In particular, we address the question of well posedness of the problem. Then, the identification of the initial data is formulated as a minimization problem combining the output least squares method and the Tikhonov regularization. Finally, numerical results are provided to show the performance of the proposed approach.