Lipschitz stability for backward heat equation with application to fluorescence microscopy

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dc.catalogadorpau
dc.contributor.authorArratia, Pablo
dc.contributor.authorCourdurier Bettancourt, Matías Alejandro
dc.contributor.authorCueva, Evelyn
dc.contributor.authorOsses, Axel
dc.contributor.authorPalacios Farias, Benjamin Pablo
dc.date.accessioned2023-08-04T21:22:22Z
dc.date.available2023-08-04T21:22:22Z
dc.date.issued2021
dc.description.abstractIn this work we study a Lipschitz stability result in the reconstruction of a compactly supported initial temperature for the heat equation in R-n, from measurements along a positive time interval and over an open set containing its support. We employ a nonconstructive method which ensures the existence of the stability constant, but it is not explicit in terms of the parameters of the problem. The main ingredients in our method are the compactness of support of the initial condition and the explicit dependency of solutions to the heat equation with respect to it. By means of Carleman estimates we obtain an analogous result for the case when the observation is made along an exterior region omega x (t, T), such that the unobserved part R-n\omega is bounded. In the latter setting, the method of Carleman estimates gives a general conditional logarithmic stability result when initial temperatures belong to a certain admissible set, without the assumption of compactness of support and allowing an explicit stability constant. Furthermore, we apply these results to deduce similar stability inequalities for the heat equation in R and with measurements available on a curve contained in Rx[0,infinity), leading to the derivation of stability estimates for an inverse problem arising in 2D fluorescence microscopy. In order to further understand this Lipschitz stability, in particular, the magnitude of its stability constant with respect to the parameters of the problem, a numerical reconstruction is presented based on the construction of a linear system for the inverse problem in fluorescence microscopy. We investigate the stability constant by analyzing the condition number of the corresponding matrix.
dc.description.funderANID-FONDECYT
dc.description.funderBasal Program
dc.description.funderFONDAP
dc.description.funderMathAmsud
dc.description.funderANID Millennium Science Initiative Program
dc.format.extent31 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1137/20M1374183
dc.identifier.eissn1095-7154
dc.identifier.issn0036-1410
dc.identifier.urihttps://doi.org/10.1137/20M1374183
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/74354
dc.identifier.wosidWOS:000749346300030
dc.information.autorucFacultad de Matemáticas; Courdurier Bettancourt, Matías Alejandro; 0000-0002-2161-0356; 1007892
dc.information.autorucFacultad de Matemáticas; Palacios Farias, Benjamin Pablo; 0000-0003-1671-5839; 1209192
dc.issue.numero5
dc.language.isoen
dc.nota.accesoContenido parcial
dc.pagina.final5978
dc.pagina.inicio5948
dc.publisherSIAM PUBLICATIONS
dc.revistaSIAM JOURNAL ON MATHEMATICAL ANALYSIS
dc.rightsacceso restringido
dc.subjectBackward heat equation
dc.subjectLipschitz stability
dc.subjectInverse problem
dc.subjectFluorescence microscopy
dc.subjectNull-Controllability
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.titleLipschitz stability for backward heat equation with application to fluorescence microscopy
dc.typeartículo
dc.volumen53
sipa.codpersvinculados1007892
sipa.codpersvinculados1209192
sipa.indexWOS
sipa.trazabilidadWOS;18-03-2022
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