An inverse problem for a one-dimensional time-fractional diffusion problem

Handle URI:
http://hdl.handle.net/10754/597536
Title:
An inverse problem for a one-dimensional time-fractional diffusion problem
Authors:
Jin, Bangti; Rundell, William
Abstract:
We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique identifiability of the potential is shown for two cases, i.e. the flux at one end and the net flux, provided that the set of input sources forms a complete basis in L 2(0, 1). An algorithm of the quasi-Newton type is proposed for the efficient and accurate reconstruction of the coefficient from finite data, and the injectivity of the Jacobian is discussed. Numerical results for both exact and noisy data are presented. © 2012 IOP Publishing Ltd.
Citation:
Jin B, Rundell W (2012) An inverse problem for a one-dimensional time-fractional diffusion problem. Inverse Problems 28: 075010. Available: http://dx.doi.org/10.1088/0266-5611/28/7/075010.
Publisher:
IOP Publishing
Journal:
Inverse Problems
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
26-Jun-2012
DOI:
10.1088/0266-5611/28/7/075010
Type:
Article
ISSN:
0266-5611; 1361-6420
Sponsors:
This work is supported by award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and NSF award DMS-0715060.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorJin, Bangtien
dc.contributor.authorRundell, Williamen
dc.date.accessioned2016-02-25T12:41:38Zen
dc.date.available2016-02-25T12:41:38Zen
dc.date.issued2012-06-26en
dc.identifier.citationJin B, Rundell W (2012) An inverse problem for a one-dimensional time-fractional diffusion problem. Inverse Problems 28: 075010. Available: http://dx.doi.org/10.1088/0266-5611/28/7/075010.en
dc.identifier.issn0266-5611en
dc.identifier.issn1361-6420en
dc.identifier.doi10.1088/0266-5611/28/7/075010en
dc.identifier.urihttp://hdl.handle.net/10754/597536en
dc.description.abstractWe study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique identifiability of the potential is shown for two cases, i.e. the flux at one end and the net flux, provided that the set of input sources forms a complete basis in L 2(0, 1). An algorithm of the quasi-Newton type is proposed for the efficient and accurate reconstruction of the coefficient from finite data, and the injectivity of the Jacobian is discussed. Numerical results for both exact and noisy data are presented. © 2012 IOP Publishing Ltd.en
dc.description.sponsorshipThis work is supported by award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and NSF award DMS-0715060.en
dc.publisherIOP Publishingen
dc.titleAn inverse problem for a one-dimensional time-fractional diffusion problemen
dc.typeArticleen
dc.identifier.journalInverse Problemsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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