Exact controllability for the wave equation in domains with variable boundary.
Exact controllability in fluid – solid structure: The Helmholtz model
A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability...
Exact controllability in fluid–solid structure : the Helmholtz model
A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results....
Exact controllability in projections for three-dimensional Navier–Stokes equations
Exact controllability in short time for the wave equation
Exact controllability of a non-linear generalized damped wave equation: Application to the sine-Gordon equation.
Exact controllability of a pluridimensional coupled problem.
We set a coupled boundary value problem between two domains of different dimension. The first one is the unit cube of Rn, n C [2,3], with a crack and the second one is the crack. this problem comes from Ciarlet et al. (1989), that obtained an analogous coupled problem. We show that the solution has singularities due to the crack. As in Grisvard (1989), we adapt the Hilbert uniqueness method of J.-L. Lions (1968,1988) in order to obtain the exact controllability of the associated wave equation with...
Exact controllability of the 1-d wave equation from a moving interior point
We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.
Exact controllability of the Euler-Bernoulli equation with -control only in the Dirichlet Boundary condition
The paper studies the problem of exact controllability of the Euler- Bernoulli equation in a cylinder of , via boundary controls acting on its lateral surface.
Exact controllability of the radial solutions of the semilinear wave equation in R3.
The exact internal controllability of the radial solutions of a semilinear heat equation in R3 is proved. The result applies for nonlinearities that are of an order smaller than |s| logp |s| at infinity for 1 ≤ p < 2. The method of the proof combines HUM and a fixed point technique.
Exact controllability of the wave equation in a thin domain with a wave-like boundary. (Contrôlabilité exacte de l'équation des ondes dans un domaine mince à frontière ondulée.)
Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients
In this paper we study the boundary exact controllability for the equation when the control action is of Dirichlet-Neumann form and is a bounded domain in . The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.
Exact controllability of the wave equation with Neumann boundary condition and time-dependent coefficients
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...
Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion...
Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion...
Exact distributed controllability for the semilinear wave equation.
Exact internal controllability of the elasticity system.
Exact linear lumping in abstract spaces.
Exact multiplicity of positive solutions for a class of semilinear equations on a ball.