The determination of an unknown boundary condition in a fractional diffusion equation Academic Article uri icon

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.

published proceedings

  • Applicable Analysis

author list (cited authors)

  • Rundell, W., Xu, X., & Zuo, L.

citation count

  • 48

complete list of authors

  • Rundell, William||Xu, Xiang||Zuo, Lihua

publication date

  • July 2013