No. 2023.14
Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws – A Case Study
F. Thein
Subject: Lyapunov stability, control of PDEs, IBVP for hyperbolic PDE systems
Abstract
In a recent work we studied a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $L^2$ for the arising system using a suitable feedback control. The aim of the present work is to show how this approach can be applied to a particular system. Moreover we present numerical results supporting the theoretical results.