An inverse source identification by nonlinear optimization in a two-dimensional hyperbolic problem

Abstract

This study deals with the identification of source function from final time state observation in a two-dimensional hyperbolic problem. The solution to the direct problem is obtained by the weak solution approach and finite element method. In the part of the inverse problem, the trust-region method and Levenberg–Marquardt method, which are nonlinear least-squares optimization methods, are used for the identification of source function. The findings are presented with numerical examples.

KEYWORDS:

• Inverse problems
• hyperbolic equations
• finite elements method
• optimization

Mathematical Subject classifications:

• 34M50
• 35L50
• 65M60
• 65K10

Acknowledgements

We are very grateful to the reviewers for their comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).