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- Title
An inverse problem for a semi-linear wave equation: A numerical study.
- Authors
Lassas, Matti; Liimatainen, Tony; Potenciano-Machado, Leyter; Tyni, Teemu
- Abstract
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $ 1+1 $ dimensions. We develop a numerical scheme to determine the potential from a noisy Dirichlet-to-Neumann map on the lateral boundary. The scheme is based on the recent higher order linearization method employed in [23]. We also present an approach to numerically estimating two-dimensional derivatives of noisy data via Tikhonov regularization. The methods are tested using synthetic noisy measurements of the Dirichlet-to-Neumann map. Various examples of reconstructions of the potential functions are given.
- Subjects
INVERSE problems; NONLINEAR wave equations; TIKHONOV regularization; QUADRATIC equations; WAVE equation; POTENTIAL functions
- Publication
Inverse Problems & Imaging, 2024, Vol 18, Issue 1, pN.PAG
- ISSN
1930-8337
- Publication type
Article
- DOI
10.3934/ipi.2023022