Inverse problems of determining sources of the fractional partial differential equations
Yikan LiuGraduate School of Mathematical Sciences The University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, JapanZhiyuan LiSchool of Mathematics and Statistics Shandong University of Technology Zibo, Shandong 255049, ChinaMasahiro YamamotoGraduate School of Mathematical Sciences The University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
2019en
ABI
Abstract
In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1. determination of time-dependent functions in interior source terms 2. determination of space-dependent functions in interior source terms 3. determination of time-dependent functions appearing in boundary conditions
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