Exact Controllability for the Wave Equation on a Graph with Cycle and Delta-Prime Vertex Conditions

2022/10/07 by Sergei Avdonin, Avdonin, Sergei, Julian Edward +3
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2210.03790

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.

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