Global uniqueness in an inverse problem for time fractional diffusion equations. (English) Zbl 1376.35099
This paper deals with the study of an initial boundary value problem with non-homogeneous Dirichlet data and driven by the weighted Laplace-Beltrami differential operator. The main results of this paper establish uniqueness properties for two inverse problems associated to the initial boundary value problem. These theorems correspond to known compact subsets of the Euclidean space, respectively to an unknown Riemannian manifold to be determined. The first setting is not contained in the second one. However, in the second case, the manifold and all the other unknown coefficients are assumed to be smooth, while in the first case the regularity assumptions are relaxed considerably. The proofs combine several tools, including the unique continuation principle for analytic functions, the spectral Hassell-Tao inequality, the normal derivative representation formula, and arguments on holomorphic functions.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
MSC:
| 35R30 | Inverse problems for PDEs |
| 35R11 | Fractional partial differential equations |
| 58J99 | Partial differential equations on manifolds; differential operators |
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