Identification of an unknown spatial source function in a multidimensional hyperbolic partial differential equation with interior degeneracy.

A reconstruction of an unknown source function is considered for hyperbolic partial differential equations with interior degeneracy. We identify the spatial element of the source term of a degenerate wave equation using the final observation data. The existence and uniqueness of the direct problem with interior degeneracy within the spatial domain are stated and proved. The inverse problem can be formulated as a nonlinear optimization problem and the unknown source term can be characterized as the solution to a minimization problem. The Tikhonov regularization technique is employed to accomplish the inclusion of noise in the input data, based on the insertion of the regularization term into the cost functional. The conjugate gradient algorithm in conjunction with Morozov's discrepancy principle as a stopping criterion is then utilized to develop an iterative reconstruction procedure. Finally, some numerical simulation results are provided to show the performance of the proposed scheme in one and two dimensions. [ABSTRACT FROM AUTHOR]