### Sobre la aproximación numérica de un problema de control geométrico.

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This paper deals with the distributed and boundary controllability of the so called Leray- model. This is a regularized variant of the Navier−Stokes system ( is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray- equations are locally null controllable, with controls bounded independently of . We also prove that, if the initial data are sufficiently small, the controls converge as → 0 to a null control of the Navier−Stokes equations. We also...

This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not apply in this work the usual duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible null...

This paper deals with some inverse and control problems for the Navier-Stokes and related systems. We will focus on some particular aspects that have recently led to interesting (theoretical and numerical) results: geometric inverse problems, Eulerian and Lagrangian controllability and vortex reduction oriented to shape optimization.

This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form $\frac{\partial y}{\partial n}+f\left(y\right)=0$. We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one...

In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form $\frac{\partial y}{\partial n}+\beta \phantom{\rule{0.166667em}{0ex}}y=0$. We consider distributed controls with support in a small set and nonregular coefficients $\beta =\beta (x,t)$. For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.

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