# American Institute of Mathematical Sciences

December  2011, 1(4): 509-518. doi: 10.3934/mcrf.2011.1.509

## Inverse source problem with a final overdetermination for a fractional diffusion equation

 1 Mathematical Science & Technology Research Lab, Advanced Technology Research Laboratories, Technical Development Bureau, Nippon Steel Corporation, 20-1 Shintomi, Futtsu, Chiba 293-8511, Japan 2 Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914

Received  December 2010 Revised  May 2011 Published  November 2011

For a time fractional diffusion equation with source term, we discuss an inverse problem of determining a spatially varying function of the source by final overdetermining data. We prove that this inverse problem is well-posed in the Hadamard sense except for a discrete set of values of diffusion constants.
Citation: Kenichi Sakamoto, Masahiro Yamamoto. Inverse source problem with a final overdetermination for a fractional diffusion equation. Mathematical Control & Related Fields, 2011, 1 (4) : 509-518. doi: 10.3934/mcrf.2011.1.509
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