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arXiv · 2604.05054

Global boundary stabilization of 1d systems of scalar conservation laws

Georges Bastin·Jean-Michel Coron·Amaury Hayat
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Abstract

We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the well-posedness of the system in the space of $L^{\infty}$ entropy solutions. Our second contribution provides a set of sufficient dissipative conditions on the boundary coupling that ensure global exponential stability in the $L^1$ and $L^\infty$ norms.

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Georges Bastin, Jean-Michel Coron, Amaury Hayat. 2026-04-06. Global boundary stabilization of 1d systems of scalar conservation laws. https://arxiv.org/abs/2604.05054

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