Global uniqueness in an inverse problem for time fractional diffusion equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Kian, Y.¹  Oksanen, L.²  Soccorsi, E.¹  Yamamoto, M.³ 

[1] Aix Marseille Univ, Univ Toulon, CNRS, CPT, Marseille, France

[2] UCL, Dept Math, Gower St, London WC1E 6BT, England

[3] Univ Tokyo, Dept Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 153, Japan

关键词: Inverse problems;    Fractional diffusion equation;    Partial data;    Uniqueness result;   

DOI  :  10.1016/j.jde.2017.09.032

来源: Elsevier

【 摘 要 】

Given (M, g), a compact connected Riemannian manifold of dimension d >= 2, with boundary partial derivative M, we consider an initial boundary value problem for a fractional diffusion equation on (0, T) x M, T > 0, with time-fractional Caputo derivative of order alpha is an element of (0, 1) U (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 am at fixed time. In the flat case where M is a compact subset of R-d, two out the three coefficients rho (density), alpha (conductivity) and q (potential) appearing in the equation p partial derivative(alpha)(t) u - div (alpha del u) + qu = 0 on (0, T) x M are recovered simultaneously. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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