Well-posedness and inverse problems for semilinear nonlocal wave equations

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...

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Detalles Bibliográficos
Autores: Lin, Yi-Hsuan, Tyni, Teemu, Zimmermann, Philipp
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2024
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:dnet:recercat____::268d96c08786fd3a14f15d90c98febff
Acceso en línea:https://hdl.handle.net/2445/229535
Access Level:acceso abierto
Palabra clave:Problemes inversos (Equacions diferencials)
Equacions en derivades parcials
Funcions de variables reals
Anàlisi harmònica
Inverse problems (Differential equations)
Partial differential equations
Functions of real variables
Harmonic analysis
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repository_id_str
spelling Well-posedness and inverse problems for semilinear nonlocal wave equationsLin, Yi-HsuanTyni, TeemuZimmermann, PhilippProblemes inversos (Equacions diferencials)Equacions en derivades parcialsFuncions de variables realsAnàlisi harmònicaInverse problems (Differential equations)Partial differential equationsFunctions of real variablesHarmonic analysisThis 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 $n \in \mathbb{N}$.Elsevier2026202620242026info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion19 p.application/pdfhttps://hdl.handle.net/2445/229535Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: https://doi.org/10.1016/j.na.2024.113601Nonlinear Analysis: Theory, Methods & Applications, 2024, vol. 247https://doi.org/10.1016/j.na.2024.113601cc-by-nc (c) Lin, Yi-Hsuan et al., 2024http://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:dnet:recercat____::268d96c08786fd3a14f15d90c98febff2026-05-29T05:05:01Z
dc.title.none.fl_str_mv Well-posedness and inverse problems for semilinear nonlocal wave equations
title Well-posedness and inverse problems for semilinear nonlocal wave equations
spellingShingle Well-posedness and inverse problems for semilinear nonlocal wave equations
Lin, Yi-Hsuan
Problemes inversos (Equacions diferencials)
Equacions en derivades parcials
Funcions de variables reals
Anàlisi harmònica
Inverse problems (Differential equations)
Partial differential equations
Functions of real variables
Harmonic analysis
title_short Well-posedness and inverse problems for semilinear nonlocal wave equations
title_full Well-posedness and inverse problems for semilinear nonlocal wave equations
title_fullStr Well-posedness and inverse problems for semilinear nonlocal wave equations
title_full_unstemmed Well-posedness and inverse problems for semilinear nonlocal wave equations
title_sort Well-posedness and inverse problems for semilinear nonlocal wave equations
dc.creator.none.fl_str_mv Lin, Yi-Hsuan
Tyni, Teemu
Zimmermann, Philipp
author Lin, Yi-Hsuan
author_facet Lin, Yi-Hsuan
Tyni, Teemu
Zimmermann, Philipp
author_role author
author2 Tyni, Teemu
Zimmermann, Philipp
author2_role author
author
dc.subject.none.fl_str_mv Problemes inversos (Equacions diferencials)
Equacions en derivades parcials
Funcions de variables reals
Anàlisi harmònica
Inverse problems (Differential equations)
Partial differential equations
Functions of real variables
Harmonic analysis
topic Problemes inversos (Equacions diferencials)
Equacions en derivades parcials
Funcions de variables reals
Anàlisi harmònica
Inverse problems (Differential equations)
Partial differential equations
Functions of real variables
Harmonic analysis
description 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 $n \in \mathbb{N}$.
publishDate 2024
dc.date.none.fl_str_mv 2024
2026
2026
2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/229535
url https://hdl.handle.net/2445/229535
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1016/j.na.2024.113601
Nonlinear Analysis: Theory, Methods & Applications, 2024, vol. 247
https://doi.org/10.1016/j.na.2024.113601
dc.rights.none.fl_str_mv cc-by-nc (c) Lin, Yi-Hsuan et al., 2024
http://creativecommons.org/licenses/by-nc/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc (c) Lin, Yi-Hsuan et al., 2024
http://creativecommons.org/licenses/by-nc/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 19 p.
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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