Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation

Handle URI:
http://hdl.handle.net/10754/600136
Title:
Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation
Authors:
Luchko, Yuri; Rundell, William; Yamamoto, Masahiro; Zuo, Lihua
Abstract:
In this paper, we consider a reaction-diffusion problem with an unknown nonlinear source function that has to be determined from overposed data. The underlying model is in the form of a time-fractional reaction-diffusion equation and the work generalizes some known results for the inverse problems posed for PDEs of parabolic type. For the inverse problem under consideration, a uniqueness result is proved and a numerical algorithm with some theoretical qualification is presented in the one-dimensional case. The key both to the uniqueness result and to the numerical algorithm relies on the maximum principle which has recently been shown to hold for the fractional diffusion equation. In order to show the effectiveness of the proposed method, results of numerical simulations are presented. © 2013 IOP Publishing Ltd.
Citation:
Luchko Y, Rundell W, Yamamoto M, Zuo L (2013) Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation. Inverse Problems 29: 065019. Available: http://dx.doi.org/10.1088/0266-5611/29/6/065019.
Publisher:
IOP Publishing
Journal:
Inverse Problems
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
30-May-2013
DOI:
10.1088/0266-5611/29/6/065019
Type:
Article
ISSN:
0266-5611; 1361-6420
Sponsors:
WR was supported by grant NSF DMS-0715060. WR and LZ acknowledge support from award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). All the authors thank the anonymous referees for very valuable comments.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorLuchko, Yurien
dc.contributor.authorRundell, Williamen
dc.contributor.authorYamamoto, Masahiroen
dc.contributor.authorZuo, Lihuaen
dc.date.accessioned2016-02-28T06:43:28Zen
dc.date.available2016-02-28T06:43:28Zen
dc.date.issued2013-05-30en
dc.identifier.citationLuchko Y, Rundell W, Yamamoto M, Zuo L (2013) Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation. Inverse Problems 29: 065019. Available: http://dx.doi.org/10.1088/0266-5611/29/6/065019.en
dc.identifier.issn0266-5611en
dc.identifier.issn1361-6420en
dc.identifier.doi10.1088/0266-5611/29/6/065019en
dc.identifier.urihttp://hdl.handle.net/10754/600136en
dc.description.abstractIn this paper, we consider a reaction-diffusion problem with an unknown nonlinear source function that has to be determined from overposed data. The underlying model is in the form of a time-fractional reaction-diffusion equation and the work generalizes some known results for the inverse problems posed for PDEs of parabolic type. For the inverse problem under consideration, a uniqueness result is proved and a numerical algorithm with some theoretical qualification is presented in the one-dimensional case. The key both to the uniqueness result and to the numerical algorithm relies on the maximum principle which has recently been shown to hold for the fractional diffusion equation. In order to show the effectiveness of the proposed method, results of numerical simulations are presented. © 2013 IOP Publishing Ltd.en
dc.description.sponsorshipWR was supported by grant NSF DMS-0715060. WR and LZ acknowledge support from award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). All the authors thank the anonymous referees for very valuable comments.en
dc.publisherIOP Publishingen
dc.titleUniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equationen
dc.typeArticleen
dc.identifier.journalInverse Problemsen
dc.contributor.institutionTechnische Universitat Berlin, Berlin, Germanyen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionUniversity of Tokyo, Tokyo, Japanen
kaust.grant.numberKUS-C1-016-04en
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