Homogenization and Inverse Problems for Fractional Diffusion Equations
Kawamoto, Atsushi, Manabu Machida, Masahiro Yamamoto · arXiv (Cornell University) · 2023
We consider the homogenization for time-fractional diffusion equations in a periodic structure and we derive the homogenized time-fractional diffusion equation. Then we discuss the determination of the constant diffusion coefficient by minimum data. Combining the results obtained above, we investigate the inverse problems of determining the diffusion coefficient for the homogenized equations from the data in the periodic structure and vice versa, that is, we investigate the inverse problem of determining the diffusion coefficient for the periodic equations from the data in the homogenized structure.