STABILITY OF THE EQUILIBRIUM STATE FOR THE SCALAR CONSERVATION LAW WITH NONLOCAL CHARACTERISTIC VELOCITIES

Abstract

In this paper, we study input-state stability (ISS) of equilibrium for a scalar conservation law with nonlocal velocity and measurement error occurring in a high-volume reproducible system . Using the corresponding Lyapunov function, we derive sufficient and necessary conditions on ISS. We propose a numerical discretization of the scalar conservation law with nonlocal velocity and measurement error. For the proposed numerical approximation, the appropriate discrete Lyapunov function is analyzed to provide the ISS of the discrete equilibrium. For the proposed numerical approximation, the appropriate discrete Lyapunov function is analyzed to provide the ISS of the discrete equilibrium. Finally, we show computational results to confirm the theoretical conclusions.