Handle URI:
http://hdl.handle.net/10754/599471
Title:
Recovery of an initial temperature from discrete sampling
Authors:
DeVore, Ronald; Zuazua, Enrique
Abstract:
The problem of recovering the initial temperature of a body from discrete temperature measurements made at later times is studied. While this problem has a general formulation, the results of this paper are only given in the simplest setting of a finite (one-dimensional), constant coefficient, linear rod. It is shown that with a judicious placement of a thermometer on this rod, the initial temperature profile of the rod can be completely determined by later time measurements. The paper then studies the number of measurements that are needed to recover the initial profile to a prescribed accuracy and provides an optimal reconstruction algorithm under the assumption that the initial profile is in a Sobolev class. © 2014 World Scientific Publishing Company.
Citation:
DeVore R, Zuazua E (2014) Recovery of an initial temperature from discrete sampling. Mathematical Models and Methods in Applied Sciences 24: 2487–2501. Available: http://dx.doi.org/10.1142/S0218202514500262.
Publisher:
World Scientific Pub Co Pte Lt
Journal:
Mathematical Models and Methods in Applied Sciences
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Nov-2014
DOI:
10.1142/S0218202514500262
Type:
Article
ISSN:
0218-2025; 1793-6314
Sponsors:
The authors acknowledge Mourad Choulli for fruitful discussions and valuable bibliographical comments. This research was initiated when the first author was a visiting scholar at the Basque Center for Applied Mathematics, in the frame of the NUMERIWAVES AdvG of ERC. This research was supported by the Office of Naval Research Contracts ONR N00014-09-1-0107, ONR N00014-11-1-0712, ONR N00014-12-1-0561; and the National Science Foundation Grant DMS 12 22390. This publication is based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The work of the second author was supported by Grant MTM2011-29306-C02-00 of the MICINN (Spain), the Advanced Grant FP7-246775 of the European Research Council Executive Agency and the Grant PI2010-04 of the Basque Government. This work was finished while the second author was visiting the Laboratoire Jacques Louis Lions with the support of the Paris City Hall "Research in Paris" program and the CIMI - Toulouse on the Excellence Chair on "PDE, Control and Numerics".
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorDeVore, Ronalden
dc.contributor.authorZuazua, Enriqueen
dc.date.accessioned2016-02-28T05:51:45Zen
dc.date.available2016-02-28T05:51:45Zen
dc.date.issued2014-11en
dc.identifier.citationDeVore R, Zuazua E (2014) Recovery of an initial temperature from discrete sampling. Mathematical Models and Methods in Applied Sciences 24: 2487–2501. Available: http://dx.doi.org/10.1142/S0218202514500262.en
dc.identifier.issn0218-2025en
dc.identifier.issn1793-6314en
dc.identifier.doi10.1142/S0218202514500262en
dc.identifier.urihttp://hdl.handle.net/10754/599471en
dc.description.abstractThe problem of recovering the initial temperature of a body from discrete temperature measurements made at later times is studied. While this problem has a general formulation, the results of this paper are only given in the simplest setting of a finite (one-dimensional), constant coefficient, linear rod. It is shown that with a judicious placement of a thermometer on this rod, the initial temperature profile of the rod can be completely determined by later time measurements. The paper then studies the number of measurements that are needed to recover the initial profile to a prescribed accuracy and provides an optimal reconstruction algorithm under the assumption that the initial profile is in a Sobolev class. © 2014 World Scientific Publishing Company.en
dc.description.sponsorshipThe authors acknowledge Mourad Choulli for fruitful discussions and valuable bibliographical comments. This research was initiated when the first author was a visiting scholar at the Basque Center for Applied Mathematics, in the frame of the NUMERIWAVES AdvG of ERC. This research was supported by the Office of Naval Research Contracts ONR N00014-09-1-0107, ONR N00014-11-1-0712, ONR N00014-12-1-0561; and the National Science Foundation Grant DMS 12 22390. This publication is based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The work of the second author was supported by Grant MTM2011-29306-C02-00 of the MICINN (Spain), the Advanced Grant FP7-246775 of the European Research Council Executive Agency and the Grant PI2010-04 of the Basque Government. This work was finished while the second author was visiting the Laboratoire Jacques Louis Lions with the support of the Paris City Hall "Research in Paris" program and the CIMI - Toulouse on the Excellence Chair on "PDE, Control and Numerics".en
dc.publisherWorld Scientific Pub Co Pte Lten
dc.subjectdiscrete time samplingen
dc.subjectFourier representationen
dc.subjectHeat equationen
dc.subjectinitial datumen
dc.subjectinversionen
dc.subjectoptimal recoveryen
dc.subjectsensingen
dc.titleRecovery of an initial temperature from discrete samplingen
dc.typeArticleen
dc.identifier.journalMathematical Models and Methods in Applied Sciencesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionBasque Center for Applied Mathematics (BCAM), Bilbao, Spainen
dc.contributor.institutionIkerbasque, the Basque Foundation for Science, Bilbao, Spainen
kaust.grant.numberKUS-C1-016-04en
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