The determination of an unknown boundary condition in a fractional diffusion equation
KAUST Grant NumberKUS-C1-016-04
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AbstractIn 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.
CitationRundell W, Xu X, Zuo L (2013) The determination of an unknown boundary condition in a fractional diffusion equation. Applicable Analysis 92: 1511–1526. Available: http://dx.doi.org/10.1080/00036811.2012.686605.
SponsorsThe 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).
PublisherInforma UK Limited