The determination of an unknown boundary condition in a fractional diffusion equation

Handle URI:
http://hdl.handle.net/10754/599893
Title:
The determination of an unknown boundary condition in a fractional diffusion equation
Authors:
Rundell, William; Xu, Xiang; Zuo, Lihua
Abstract:
In this article we consider an inverse boundary problem, in which the unknown boundary function ∂u/∂v = f(u) is to be determined from overposed data in a time-fractional diffusion equation. Based upon the free space fundamental solution, we derive a representation for the solution f as a nonlinear Volterra integral equation of second kind with a weakly singular kernel. Uniqueness and reconstructibility by iteration is an immediate result of a priori assumption on f and applying the fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. © 2013 Copyright Taylor and Francis Group, LLC.
Citation:
Rundell W, Xu X, Zuo L (2013) The determination of an unknown boundary condition in a fractional diffusion equation. Applicable Analysis 92: 1511–1526. Available: http://dx.doi.org/10.1080/00036811.2012.686605.
Publisher:
Informa UK Limited
Journal:
Applicable Analysis
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Jul-2013
DOI:
10.1080/00036811.2012.686605
Type:
Article
ISSN:
0003-6811; 1563-504X
Sponsors:
The authors acknowledge partial support from National Science Foundation grants DMS-0715060 and DMS-0900889 and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorRundell, Williamen
dc.contributor.authorXu, Xiangen
dc.contributor.authorZuo, Lihuaen
dc.date.accessioned2016-02-28T06:31:51Zen
dc.date.available2016-02-28T06:31:51Zen
dc.date.issued2013-07en
dc.identifier.citationRundell W, Xu X, Zuo L (2013) The determination of an unknown boundary condition in a fractional diffusion equation. Applicable Analysis 92: 1511–1526. Available: http://dx.doi.org/10.1080/00036811.2012.686605.en
dc.identifier.issn0003-6811en
dc.identifier.issn1563-504Xen
dc.identifier.doi10.1080/00036811.2012.686605en
dc.identifier.urihttp://hdl.handle.net/10754/599893en
dc.description.abstractIn this article we consider an inverse boundary problem, in which the unknown boundary function ∂u/∂v = f(u) is to be determined from overposed data in a time-fractional diffusion equation. Based upon the free space fundamental solution, we derive a representation for the solution f as a nonlinear Volterra integral equation of second kind with a weakly singular kernel. Uniqueness and reconstructibility by iteration is an immediate result of a priori assumption on f and applying the fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. © 2013 Copyright Taylor and Francis Group, LLC.en
dc.description.sponsorshipThe authors acknowledge partial support from National Science Foundation grants DMS-0715060 and DMS-0900889 and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherInforma UK Limiteden
dc.subjectfixed point theoryen
dc.subjectinverse boundaryen
dc.subjecttime-fractional diffusion equationen
dc.titleThe determination of an unknown boundary condition in a fractional diffusion equationen
dc.typeArticleen
dc.identifier.journalApplicable Analysisen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionFudan University, Shanghai, Chinaen
kaust.grant.numberKUS-C1-016-04en
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