Controllability for a scalar conservation law with nonlocal velocity

Abstract

In this paper, we study the state controllability and nodal profile controllability for a scalar conservation law, with a nonlocal velocity, that models a highly re-entrant manufacturing system as encountered in semi-conductor production. We first prove a local state controllability result, i.e., there exists a control that drives the solution from any given initial data to any desired final data in a certain time period, provided that the initial and final data are both close to a given equilibrium ρ ¯ ⩾ 0 . We also obtain a global state controllability result for the same system, where there is no limitation on the distance between the initial and final data. Finally, we prove a nodal profile controllability result, i.e., there exists a control under which the solution starts from any initial data reaches exactly any given out-flux over a fixed time period.