On the control of the Burgers-alpha model

Abstract

This work is devoted to proving the local null controllability of the Burgers- α model. The state is the solution to a regularized Burgers equation, where the transport term is of the form z y x , z = ( I d − α 2 ∂ 2 ∂ x 2 ) − 1 y , and α > 0 is a small parameter. We also prove some results concerning the behavior of the null controls and associated states as α → 0 + .