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2024-10-01

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cc-by-nc (c) Lin, Yi-Hsuan et al., 2024
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/229535

Well-posedness and inverse problems for semilinear nonlocal wave equations

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Recurs relacionat

https://doi.org/10.1016/j.na.2024.113601

Resum

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 $f(x, u)$ 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 $n \in \mathbb{N}$.

Matèries

Problemes inversos (Equacions diferencials), Equacions en derivades parcials, Funcions de variables reals, Anàlisi harmònica

Matèries (anglès)

Inverse problems (Differential equations), Partial differential equations, Functions of real variables, Harmonic analysis

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citació

LIN, Yi-Hsuan, TYNI, Teemu and ZIMMERMANN, Philipp. Well-posedness and inverse problems for semilinear nonlocal wave equations. Nonlinear Analysis: Theory. Methods & Applications. Vol.  2024, num. 247. ISSN 0362-546X. [consulted: 28 of June of 2026]. Available at: https://hdl.handle.net/2445/229535

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