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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 7
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Articles

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

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Pages 1511-1526 | Received 22 Dec 2011, Accepted 16 Apr 2012, Published online: 23 May 2012
 

Abstract

In this article we consider an inverse boundary problem, in which the unknown boundary function 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.

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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).

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