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

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.

authors

• Rundell, William
• Zuo, Lihua

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

• January 2013

publisher

• Taylor & Francis  Publisher

published in

• Applicable Analysis: an international journal  Journal

keywords

• Fixed Point Theory
• Inverse Boundary
• Time-fractional Diffusion Equation

Digital Object Identifier (DOI)

• 10.1080/00036811.2012.686605

start page

• 1511

end page

• 1526

volume

• 92

issue

• 7

URL

• http://dx.doi.org/10.1080/00036811.2012.686605