Well-posedness and inverse problems for semilinear nonlocal wave equations
Lin, Yi Hsuan; Tyni, Teemu; Zimmermann, Philipp (2024-07-01)
Elsevier
01.07.2024
Lin, Y.-H., Tyni, T., & Zimmermann, P. (2024). Well-posedness and inverse problems for semilinear nonlocal wave equations. Nonlinear Analysis, 247, 113601. https://doi.org/10.1016/j.na.2024.113601
https://creativecommons.org/licenses/by-nc/4.0/
© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
https://creativecommons.org/licenses/by-nc/4.0/
© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
https://creativecommons.org/licenses/by-nc/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202407085143
https://urn.fi/URN:NBN:fi:oulu-202407085143
Tiivistelmä
Abstract
This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main challenge is due to the low regularity of the solutions of linear nonlocal wave equations. We then turn to an inverse problem of recovering the nonlinearity of the equation. More precisely, we show that the exterior Dirichlet-to-Neumann map uniquely determines homogeneous nonlinearities of the form under certain growth conditions. On the other hand, we also prove that initial data can be determined by using passive measurements under certain nonlinearity conditions. The main tools used for the inverse problem are the unique continuation principle of the fractional Laplacian and a Runge approximation property. The results hold for any spatial dimension 𝑛 ∈ N.
This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main challenge is due to the low regularity of the solutions of linear nonlocal wave equations. We then turn to an inverse problem of recovering the nonlinearity of the equation. More precisely, we show that the exterior Dirichlet-to-Neumann map uniquely determines homogeneous nonlinearities of the form under certain growth conditions. On the other hand, we also prove that initial data can be determined by using passive measurements under certain nonlinearity conditions. The main tools used for the inverse problem are the unique continuation principle of the fractional Laplacian and a Runge approximation property. The results hold for any spatial dimension 𝑛 ∈ N.
Kokoelmat
- Avoin saatavuus [34516]
Ellei muuten mainita, aineiston lisenssi on https://creativecommons.org/licenses/by-nc/4.0/