Abstract
Time-fractional diffusion equations are of great interest and importance on describing the power law decay for diffusion in porous media. In this paper, to identify the diffusion rate, i.e., the heterogeneity of medium, the authors consider an inverse coefficient problem utilizing finite measurements and obtain a local Hölder type conditional stability based upon two Carleman estimates for the corresponding differential equations of integer orders.
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This work was supported by the National Natural Science Foundation of China (No. 11101093) and Shanghai Science and Technology Commission (Nos. 11ZR1402800, 11PJ1400800).
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Ren, C., Xu, X. Local stability for an inverse coefficient problem of a fractional diffusion equation. Chin. Ann. Math. Ser. B 35, 429–446 (2014). https://doi.org/10.1007/s11401-014-0833-0
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DOI: https://doi.org/10.1007/s11401-014-0833-0