A1 Journal article (refereed)
Uniqueness, reconstruction and stability for an inverse problem of a semi-linear wave equation (2022)

Lassas, M., Liimatainen, T., Potenciano-Machado, L., & Tyni, T. (2022). Uniqueness, reconstruction and stability for an inverse problem of a semi-linear wave equation. Journal of Differential Equations, 337, 395-435. https://doi.org/10.1016/j.jde.2022.08.010

JYU authors or editors

Publication details

All authors or editors: Lassas, Matti; Liimatainen, Tony; Potenciano-Machado, Leyter; Tyni, Teemu

Journal or series: Journal of Differential Equations

ISSN: 0022-0396

eISSN: 1090-2732

Publication year: 2022

Publication date: 26/08/2022

Volume: 337

Pages range: 395-435

Publisher: Elsevier

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1016/j.jde.2022.08.010

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/82906

Abstract

We consider the recovery of a potential associated with a semi-linear wave equation on Rn+1, n≥1. We show that an unknown potential a(x,t) of the wave equation □u+aum=0 can be recovered in a Hölder stable way from the map u|∂Ω×[0,T]↦〈ψ,∂νu|∂Ω×[0,T]〉L2(∂Ω×[0,T]). This data is equivalent to the inner product of the Dirichlet-to-Neumann map with a measurement function ψ. We also prove similar stability result for the recovery of a when there is noise added to the boundary data. The method we use is constructive and it is based on the higher order linearization. As a consequence, we also get a uniqueness result. We also give a detailed presentation of the forward problem for the equation □u+aum=0.

Keywords: inverse problems; partial differential equations

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 2