Null controllability of a parabolic system with a cubic coupling term

We consider a system of two parabolic equations with a forcing term present in one equation and a cubic coupling term in the other one. We prove that the system is locally null controllable.Comment: 24 page

A parabolic approach to the control of opinion spreading

We analyze the problem of controlling to consensus a nonlinear system modeling opinion spreading. We derive explicit exponential estimates on the cost of approximately controlling these systems to consensus, as a function of the number of agents N and the control time-horizon T. Our strategy makes use of known results on the controllability of spatially discretized semilinear parabolic equations. Both systems can be linked through time-rescalin