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We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in R 2. Piecewise linear finite elements are used to… (More)

We study the exponential stabilization of the linearized Navier-Stokes equations around an unstable stationary solution, by means of a feedback boundary control, in dimension 2 or 3. The feedback law is determined by solving a Linear-Quadratic control problem. We do not assume that the normal component of the control is equal to zero. In that case the state… (More)

- Jean-Pierre Raymond, Laetitia Thevenet, LAETITIA THEVENET
- 2010

We study the boundary stabilization of the two-dimensional Navier-Stokes equations about an unstable stationary solution by controls of finite dimension in feedback form. The main novelty is that the linear feedback control law is determined by solving an optimal control problem of finite dimension. More precisely, we show that, to stabilize locally the… (More)

We study the exponential stabilization of the linearized Navier-Stokes equations around an unstable stationary solution, by means of a feedback boundary control, in dimension 2 or 3. The feedback law is determined by solving a Linear-Quadratic control problem. We do not assume that the normal component of the control is equal to zero. In that case the state… (More)

We consider optimal control problems for hyperbolic equations with controls in Neu-mann boundary conditions with pointwise constraints on the control and state functions. Focusing on the multidimensional wave equation with a nonlinear term, we derive new necessary optimality conditions in the form of a pointwise Pontryagin Maximum Principle for the… (More)

We study a system coupling the incompressible Navier-Stokes equations in a 2D rectangular type domain with a damped Euler-Bernoulli beam equation, where the beam is a part of the upper boundary of the domain occupied by the fluid. Due to the deformation of the beam the fluid domain depends on time. We prove that this system is exponentially stabilizable,… (More)