Analyzes boundary feedback conditions for ensuring global exponential stability in 1D systems of conservation laws, suggesting implications for control theory.
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∞ entropy solutions. Our second contribution provides a set of sufficient dissipative conditions on the boundary coupling that ensure global exponential stability in the L¹ and L^∞ norms.
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Bastin et al. (2026) studied this question.
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