Global Controllability of Nonviscous and Viscous Burgers-Type Equations

In this paper, we deal with both nonviscous and viscous Burgers type equations on a bounded interval. We study the global exact controllability of these equations when we have three controls: one control is the right member of the equation and is constant with respect to the space variable, the two others are the boundary values. In a first time, we are interested in nonviscous Burgers type equations and we prove their global exact controllability for every time T > 0 with such controls thanks to the return method. Then we prove the global exact controllability of the viscous Burgers equation, for every time T > 0.