Theoretical analysis and control results for the Fitzhugh-Nagumo equation.
Sobre la aproximación numérica de un problema de control geométrico.
Null and approximate controllability for weakly blowing up semilinear heat equations
Some new existence results for the variable density Navier-Stokes equations
A numerical study of some questions in vortex rings theory
Uniform local null control of the Leray-α model
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...
Numerical controllability of the wave equation through primal methods and Carleman estimates
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...
Some theoretical results concerning non newtonian fluids of the Oldroyd kind
An optimal control problem for a generalized Boussinesq model: The time dependent case.
Some inverse and control problems for fluids
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.
Null controllability of the heat equation with boundary Fourier conditions: the linear case
In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form . We consider distributed controls with support in a small set and nonregular coefficients . 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.
Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case
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 . 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...
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