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

William Rundell, Xiang Xu, Lihua Zuo

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)1511-1526
Number of pages16
JournalApplicable Analysis
Volume92
Issue number7
DOIs
StatePublished - Jul 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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