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arXiv · 2203.09427

An inverse problem for a semi-linear wave equation: a numerical study

Matti Lassas·Tony Liimatainen·Leyter Potenciano-Machado·Teemu Tyni
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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 [20]. 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.

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Matti Lassas, Tony Liimatainen, Leyter Potenciano-Machado, Teemu Tyni. 2022-03-17. An inverse problem for a semi-linear wave equation: a numerical study. https://arxiv.org/abs/2203.09427

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