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arXiv · 2506.10495

Controllability and Stabilization of a Wave-Heat Cascade System

Hugo Lhachemi·Christophe Prieur·Emmanuel Trélat
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Abstract

Considering a wave-reaction-diffusion PDE cascade system with wave Neumann control, we first establish controllability properties in a suitable Hilbert space depending on the coupling cascade term. This is done by deriving an observability inequality for the dual problem by resorting to an Ingham-M{\"u}ntz inequality. Second, we design an explicit output feedback control strategy for the actual stabilization of the PDE cascade. The key property is that the underlying operator is a Riesz-spectral operator.

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Hugo Lhachemi, Christophe Prieur, Emmanuel Trélat. 2025-06-12. Controllability and Stabilization of a Wave-Heat Cascade System. https://arxiv.org/abs/2506.10495

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