Inverse source problems for a wave equation with involution

Abstract

Inverse source problems for a wave equation with involution A class of inverse problems for a wave equation with involution is considered for cases of two different boundary conditions, namely, Dirichlet and Neumann boundary conditions. The existence and uniqueness of solutions of these problems are proved. The solutions are obtained in the form of series expansion using a set of appropriate orthogonal basises for each problem. Convergence of the obtained solutions is also justified.