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.
Bastin et al. (Mon,) studied this question.