Electron. J. Differential Equations, Vol. 2017 (2017), No. 119, pp. 1-19.

An inverse source problem of the Poisson equation with Cauchy data

Ji-Chuan Liu

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 ill-posed, 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; trust-region-reflective algorithm; Poisson equation; ill-posed problem.

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Ji-Chuan Liu
School of Mathematics
China University of Mining and Technology
Xuzhou, Jiangsu 221116, China
email: liujichuan2003@126.com

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