Exact Controllability for the Wave Equation on a Graph with Cycle and Delta-Prime Vertex Conditions
Optimization and Control
2022-10-11 v1
Abstract
Exact controllability for the wave equation on a metric graph consisting of a cycle and two attached edges is proven. One boundary and one internal control are used. At the internal vertices, delta-prime conditions are satisfied. As a second example, we examine a tripod controlled at the root and the junction, while the leaves are fixed. These examples are key to understanding controllability properties in general metric graphs.
Keywords
Cite
@article{arxiv.2210.03790,
title = {Exact Controllability for the Wave Equation on a Graph with Cycle and Delta-Prime Vertex Conditions},
author = {Sergei Avdonin and Julian Edward and Gunter Leugering},
journal= {arXiv preprint arXiv:2210.03790},
year = {2022}
}