Spatial decay of perturbations in hyperbolic equations with optimal boundary control

Benedikt Oppeneiger; Manuel Schaller; Karl Worthmann

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arXiv · 2502.11975

Spatial decay of perturbations in hyperbolic equations with optimal boundary control

Benedikt Oppeneiger·Manuel Schaller·Karl Worthmann

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Abstract

Recently, domain-uniform stabilizability and detectability has been the central assumption %in order robustness results on the to ensure robustness in the sense of exponential decay of spatially localized perturbations in optimally controlled evolution equations. In the present paper we analyze a chain of transport equations with boundary and point controls with regard to this property. Both for Dirichlet and Neumann boundary and coupling conditions, we show a necessary and sufficient criterion on control domains which allow for the domain-uniform stabilization of this equation. We illustrate the results by means of a numerical example.

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Benedikt Oppeneiger, Manuel Schaller, Karl Worthmann. 2025-02-17. Spatial decay of perturbations in hyperbolic equations with optimal boundary control. https://arxiv.org/abs/2502.11975

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