Determination of time dependent factors of coefficients in fractional diffusion equations

Kenichi  Fujishiro; Yavar  Kian

doi:10.3934/mcrf.2016003

Article Contents

2016, Volume 6, Issue 2: 251-269. Doi: 10.3934/mcrf.2016003

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Determination of time dependent factors of coefficients in fractional diffusion equations

Kenichi Fujishiro^1, and
Yavar Kian^2,

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

Received: January 2015

Revised: February 2016

Published: June 2016

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Abstract

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 $t\in(0,T)$.

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Mathematics Subject Classification: Primary: 35R30, 35R11.

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