Electron. J. Differential Equations,
Vol. 2017 (2017), No. 119, pp. 119.
An inverse source problem of the Poisson equation with Cauchy data
JiChuan Liu
Abstract:
In this article, we study an inverse source problem of the
Poisson equation with Cauchy data. We want to find iterative algorithms
to detect the hidden source within a body from measurements on the boundary.
Our goal is to reconstruct the location, the size and the shape of the hidden
source. This problem is illposed, regularization techniques should be employed
to obtain the regularized solution. Numerical examples show that our proposed
algorithms are valid and effective.
Submitted October 26, 2016. Published May 4, 2017.
Math Subject Classifications: 65N20, 65N21.
Key Words: Inverse source problem; gradient descent method;
trustregionreflective algorithm; Poisson equation;
illposed problem.
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JiChuan Liu
School of Mathematics
China University of Mining and Technology
Xuzhou, Jiangsu 221116, China
email: liujichuan2003@126.com

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