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 language | English (US) |
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Pages (from-to) | 1511-1526 |
Number of pages | 16 |
Journal | Applicable Analysis |
Volume | 92 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2013 |
Externally published | Yes |