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arXiv · 2207.12006

Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws

Michael Herty·Ferdinand Thein
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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.

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Michael Herty, Ferdinand Thein. 2022-07-25. Stabilization of a Multi-Dimensional System of Hyperbolic Balance Laws. https://doi.org/10.3934/mcrf.2023033

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