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dc.contributor.authorLuchko, Yuri
dc.contributor.authorRundell, William
dc.contributor.authorYamamoto, Masahiro
dc.contributor.authorZuo, Lihua
dc.date.accessioned2016-02-28T06:43:28Z
dc.date.available2016-02-28T06:43:28Z
dc.date.issued2013-05-30
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.
dc.identifier.issn0266-5611
dc.identifier.issn1361-6420
dc.identifier.doi10.1088/0266-5611/29/6/065019
dc.identifier.urihttp://hdl.handle.net/10754/600136
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.
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.
dc.publisherIOP Publishing
dc.titleUniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation
dc.typeArticle
dc.identifier.journalInverse Problems
dc.contributor.institutionTechnische Universitat Berlin, Berlin, Germany
dc.contributor.institutionTexas A and M University, College Station, United States
dc.contributor.institutionUniversity of Tokyo, Tokyo, Japan
kaust.grant.numberKUS-C1-016-04
dc.date.published-online2013-05-30
dc.date.published-print2013-06-01


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