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

William Rundell, Xiang Xu, Lihua Zuo

Research output: Contribution to journalArticlepeer-review

43 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

Fingerprint Dive into the research topics of 'The determination of an unknown boundary condition in a fractional diffusion equation'. Together they form a unique fingerprint.

Cite this