Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws

Abstract

We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in ${\mathbb{R}}^n$. A reformulation leads to a 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. We further present examples of such systems partially based on a forming process.

Mathematical Control and Related Fields, 2023

References in corpus (2)

• On thermodynamically compatible finite volume schemes for continuum mechanics
• Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme

Cited by in corpus (2)

• Boundary feedback control for hyperbolic systems
• On the relation between approaches for boundary feedback control of hyperbolic systems