Global boundary stabilization of 1d systems of scalar conservation laws
This work addresses boundary control for conservation laws, which is incremental in applied mathematics and control theory.
The paper tackles the problem of stabilizing a system of one-dimensional scalar conservation laws with boundary feedback, establishing well-posedness in L∞ entropy solutions and proving global exponential stability in L¹ and L∞ norms under dissipative conditions.
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.