A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit

We revisit a result by Coron and Guerrero stating that the one-dimensional transport-diffusion equation ut +Mux −εuxx =0 in(0,T )×(0,L), controlled by the left Dirichlet boundary value is zero-controllable at a bounded cost as ε →0+, when T >4.3L/M ifM >0 and when T >57.2L/|M| ifM <0. By a completely different method, relying on complex analysis, we prove that this still holds when T >4.2L/M if M >0 and when T >6.1L/|M| if M <0. © 2009 Elsevier Inc. All rights reserved