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Inverse problem for fractional diffusion equation. (English) Zbl 1273.35323

Summary: We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

MSC:

35R30 Inverse problems for PDEs
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35R11 Fractional partial differential equations
35K57 Reaction-diffusion equations
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