The determination of an unknown boundary condition in a fractional diffusion equation
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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.
author list (cited authors)
Rundell, W., Xu, X., & Zuo, L.
complete list of authors
Rundell, William||Xu, Xiang||Zuo, Lihua