Kian, Y;
Oksanen, L;
Soccorsi, E;
Yamamoto, M;
(2018)
Global uniqueness in an inverse problem for time fractional diffusion equations.
Journal of Differential Equations
, 264
(2)
pp. 1146-1170.
10.1016/j.jde.2017.09.032.
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Abstract
Given (M,g), a compact connected Riemannian manifold of dimension d⩾2, with boundary ∂M, we consider an initial boundary value problem for a fractional diffusion equation on (0,T)× M, T > 0, with time-fractional Caputo derivative of order α∈(0,1)∪(1,2). We prove uniqueness in the inverse problem of determining the smooth manifold (M,g) (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ∂M at fixed time. In the “flat” case where M is a compact subset of R d , two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation ρ∂ t α u−div(a∇u)+qu=0 on (0,T)×M are recovered simultaneously.
| Type: | Article |
|---|---|
| Title: | Global uniqueness in an inverse problem for time fractional diffusion equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jde.2017.09.032 |
| Publisher version: | http://doi.org/10.1016/j.jde.2017.09.032 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Inverse problems,Fractional diffusion equation, Partial data, Uniqueness result |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1556030 |
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