The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability

Kow, Pu-Zhao; Lin, Yi-Hsuan; Wang, Jenn-Nan

doi:10.1137/21M1444941

dc.contributor.author	Kow, Pu-Zhao
dc.contributor.author	Lin, Yi-Hsuan
dc.contributor.author	Wang, Jenn-Nan
dc.date.accessioned	2023-02-02T11:39:22Z
dc.date.available	2023-02-02T11:39:22Z
dc.date.issued	2022
dc.identifier.citation	Kow, P.-Z., Lin, Y.-H., & Wang, J.-N. (2022). The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability. <i>SIAM Journal on Mathematical Analysis</i>, <i>54</i>(3), 3379-3419. <a href="https://doi.org/10.1137/21M1444941" target="_blank">https://doi.org/10.1137/21M1444941</a>
dc.identifier.other	CONVID_150970521
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/85312
dc.description.abstract	We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in the determination of the potential by the exterior Dirichlet-to-Neumann map. The main tools are the qualitative and quantitative unique continuation properties for the fractional Laplacian. For the stability, we also prove that the log type stability estimate is optimal. The log type estimate shows the striking difference between the inverse problems for the fractional and classical wave equations in the stability issue. The results hold for any spatial dimension n∈N	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Society for Industrial & Applied Mathematics (SIAM)
dc.relation.ispartofseries	SIAM Journal on Mathematical Analysis
dc.rights	In Copyright
dc.subject.other	Calder´on problem
dc.subject.other	peridynamic
dc.subject.other	fractional Laplacian
dc.subject.other	nonlocal
dc.subject.other	fractional wave equation
dc.subject.other	strong uniqueness
dc.subject.other	Runge approximation
dc.subject.other	logarithmic stability
dc.title	The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-202302021594
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	3379-3419
dc.relation.issn	0036-1410
dc.relation.numberinseries	3
dc.relation.volume	54
dc.type.version	acceptedVersion
dc.rights.copyright	© Authors, 2022
dc.rights.accesslevel	openAccess	fi
dc.subject.yso	osittaisdifferentiaaliyhtälöt
dc.subject.yso	inversio-ongelmat
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p12392
jyx.subject.uri	http://www.yso.fi/onto/yso/p27912
dc.rights.url	http://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi	10.1137/21M1444941
jyx.fundinginformation	The second author is partially supported by the Ministry of Science and Technology Taiwan, under the Columbus Program: MOST-109-2636-M-009-006, 2020-2025. The third author is partly supported by MOST 108-2115-M-002-002-MY3 and 109-2115-M-002-001-MY3.
dc.type.okm	A1