Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components

Tr¨ oltzsch, Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints. Tr¨ oltzsch, Lipschitz stability of optimal controls for

Anita and Barbu [3], for a reaction-diffusion system, and Barbu [5] for the phase field system, proved local exact controllability results by two localized (in space) control forces..

The aim of this work is to present some strategies to solve numerically controllability problems for the two-dimensional heat equation, the Stokes equations and the

In the even more recent work [10], it was shown that it can be necessary not only to look at the condensation of the eigenvalues but also to the associated eigenfunctions to obtain

This work is concerned with the null controllability of a class of 3 ⇥ 3 linear parabolic systems with non constant coefficients by a single control force or two control

Recently, in the one-dimensional case, the controllability result for parabolic equations was proven for general piecewise C 1 coefficients in [5], and for coefficients with

More recently in [AKBDGB09b], with fine tools of partial differential equations, the so- called Kalman rank condition, which characterizes the controllability of linear systems

The second class of equations is the class of accretive non-selfadjoint quadratic operators with zero singular spaces for which some sufficient geometric conditions on the