Inverse source problem for a one-dimensional degenerate hyperbolic problem

Abstract

This article focuses on solving inverse problems related to identifying spatial components in a one-dimensional degenerate hyperbolic equation. The study is critical in fields like physics, engineering, and environmental science. We establish the well-posedness of the direct problem and provide essential results on solving the inverse problem using functional minimization and Tikhonov regularization for accuracy. Two algorithms are introduced for different scenarios: a descent algorithm for cases with reference data and a "Thresholding" algorithm for situations without reference. Experimental validation shows the effectiveness of these methods in accurately recovering unknown source terms. This research advances understanding in hyperbolic equation inverse problems and provides practical tools for real-world applications.