An inverse problem for a multidimensional fractional diffusion equation

Vu Kim Tuan; Nguyen Si Hoang

doi:10.1515/anly-2015-5010

Article

An inverse problem for a multidimensional fractional diffusion equation

Vu Kim Tuan and Nguyen Si Hoang

Published/Copyright: September 11, 2015

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From the journal Analysis Volume 36 Issue 2

Abstract

We prove that the coefficients aij(x), q(x), and the domain Ω of a multidimensional fractional diffusion equation can be recovered uniquely from measurements u(b,t), t∈(t0,t1), at an arbitrary single point b inside a bounded domain Ω⊂ℝn. From the measurements we first recover infinitely many spectral data (λm,φm(x)) of the elliptic operator associated with the fractional diffusion equation. Then, the coefficients aij(x), q(x) are found from linear algebraic systems of the form Ay=b, where A is a generalized Wronskian of some set of eigenfunctions that can be shown to be nontrivial. The domain Ω is reconstructed using the first eigenfunction φ1(x).

Keywords: Inverse problems; fractional diffusion equations; single point measurements

MSC: 35R30; 34K29

Received: 2015-5-30

Accepted: 2015-7-9

Published Online: 2015-9-11

Published in Print: 2016-5-1

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Articles in the same Issue

https://doi.org/10.1515/anly-2015-5010

Keywords for this article

Inverse problems; fractional diffusion equations; single point measurements