Inverse source problem in a forced network
Abstract
We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes yield uniqueness of the two unknown elements: the source position and the emitted signal. Using graph theory, we discuss the number and location of the observation nodes. A non-iterative identification method that localizes the source node by solving a set of well posed linear systems is developped. Once the source node is localized, the emitted signal is identified using a deconvolution problem or a Fourier expansion. Numerical experiments on a five node graph confirm the feasability of the approach.
- Publication:
-
Inverse Problems
- Pub Date:
- May 2019
- DOI:
- 10.1088/1361-6420/aafcc6
- arXiv:
- arXiv:1803.04895
- Bibcode:
- 2019InvPr..35e5006C
- Keywords:
-
- network;
- wave equation;
- graph theory;
- Mathematics - Optimization and Control
- E-Print:
- doi:10.1088/1361-6420/aafcc6