# American Institute of Mathematical Sciences

June  2016, 6(2): 251-269. doi: 10.3934/mcrf.2016003

## Determination of time dependent factors of coefficients in fractional diffusion equations

 1 Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo 153, Japan 2 Aix-Marseille Université, CNRS, CPT UMR 7332, Marseille, 13288, France

Received  January 2015 Revised  February 2016 Published  April 2016

In the present paper, we consider initial-boundary value problems for partial differential equations with time-fractional derivatives which evolve in $Q=\Omega\times(0,T)$ where $\Omega$ is a bounded domain of $\mathbb{R}^d$ and $T>0$. We study the stability of the inverse problems of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at a point $x_0\in\overline{\Omega}$ for all $t\in(0,T)$.
Citation: Kenichi Fujishiro, Yavar Kian. Determination of time dependent factors of coefficients in fractional diffusion equations. Mathematical Control & Related Fields, 2016, 6 (2) : 251-269. doi: 10.3934/mcrf.2016003
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