On the cost of null-control of an artificial advection-diffusion problem

Pierre Cornilleau, Sergio Guerrero

Published 2012-06-22, updated 2013-01-24Version 2

In this paper we study the null-controllability of an artificial advection-diffusion system in dimension $n$. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.