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21. November 2024, 14:00-15:00

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Raum 314
Dolivostr. 15
64293 Darmstadt

Raum 314 , Dolivostr. 15 , 64293 Darmstadt

Veranstalter

FB Mathematik, AG Numerik

giesselmann@mathematik.tu-darmstadt.de

We are interested in the boundary feedback stabilization of multi–dimensional hyperbolic PDEs. Two cases are discussed in this talk. First we study systems with diagonal Jacobians which for example arise in the treatment of Hamilton-Jacobi equations, cf. [1]. The second case considers symmetric hyperbolic systems which satisfy a linear matrix inequality, cf. [2].
For each case a proper Lyapunov function is defined. With this we show stabilization in L2 for the arising system using a suitable feedback control. We further present several examples to highlight the capability of the approach. These also include applications from engineering sciences, i.e., a forming process and a melting process in additive manufacturing.

References
[1] M. Herty and F. Thein. Stabilization of a multi-dimensional system of hyperbolic balance
laws. Mathematical Control and Related Fields, 2023. https://doi.org/10.3934/mcrf.2023033
[2] M. Herty and F. Thein. Boundary feedback control for hyperbolic systems. ESAIM: Control,
Optimisation and Calculus of Variations, 2024. https://doi.org/10.1051/cocv/2024062

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Tags

Mathematik, Numerik