1. Identification of source terms in wave equation with dynamic boundary conditions
- Author
-
Salah‐Eddine Chorfi, Ghita El Guermai, Lahcen Maniar, and Walid Zouhair
- Subjects
Mathematics - Analysis of PDEs ,Optimization and Control (math.OC) ,General Mathematics ,General Engineering ,FOS: Mathematics ,35R30, 65M32, 35L05, 35L51, 74H75 ,Mathematics - Optimization and Control ,Analysis of PDEs (math.AP) - Abstract
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet differentiability of the Tikhonov functional is studied, and a gradient formula is obtained via the solution of an associated adjoint problem. Then, the Lipschitz continuity of the gradient is proved. Furthermore, the existence and the uniqueness for the minimization problem are discussed. Finally, some numerical experiments for the reconstruction of an internal wave force are implemented via a conjugate gradient algorithm., Comment: 19 pages, 3 figures, 3 tables
- Published
- 2022
- Full Text
- View/download PDF