572 RWTH Publication No: 850321        2022       
TITLE Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws
AUTHORS Michael Herty, Ferdinand Thein
ABSTRACT We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\R^n$. 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 L2 for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process.
DOI 10.1002/pamm.202200056
PUBLICATION Proceedings in Applied Mathematics and Mechanics
2022, 22, 1