Jean-Pierre Puel

Approximate controllability of the semilinear heat equation

This article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain Ω when the control acts on any open and nonempty subset of Ω or on a part of the boundary. In the case of both an internal and a boundary control, the approximate controllability in L P (Ω) for 1 ≦ p L ∞ . In the case of the interior control, we also prove approximate controllability in C 0 (Ω). The proof combines a variational approach to the controllability problem for linear equations and a fixed point method. We also prove that the control can be taken to be of “quasi bang-bang” form.

On a global estimate in a linear inverse hyperbolic problem

We show a global Lipschitz estimate in determining a source term in a hyperbolic equation from overdetermining data on the lateral boundary. The method is a combination of the uniqueness result by the Carleman estimate and the compactness - uniqueness argument, and is also widely applicable to the determination of source terms or coefficients in the general multidimensional case. Dedicated to Professor Takashi Kayano on his 63rd birthday

Some Controllability Results for the N -Dimensional Navier-Stokes and Boussinesq systems with N -1 scalar controls

In this paper we deal with some controllability problems for systems of the Navier--Stokes and Boussinesq kind with distributed controls supported in small sets. Our main aim is to control

Boundary Stabilization for the von Karman Equations

N

Smoothing property in multidimensional inverse hyperbolic problems: applications to uniqueness and stability

-dimensional systems (

ON THE DENSITY OF THE RANGE OF THE SEMIGROUP FOR SEMILINEAR HEAT EQUATIONS

N+1

Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems

scalar unknowns in the case of the Navier--Stokes equations) with

Boundary controllability of a stationary stokes system with linear convection observed on an interior curve

N-1

An Inverse Problem for the Schrödinger Equation

scalar control functions. In a first step, we present some global Carleman estimates for suitable adjoint problems of linearized Navier--Stokes and Boussinesq systems. In this way, we obtain null controllability properties for these systems. Then, we deduce results concerning the local exact controllability to the trajectories. We also present (global) null controllability results for some (truncated) approximations of the Navier--Stokes equations.

Local exact controllability of the Navier-Stokes system ✩

The boundary stabilization of a nonlinear plate model is studied. The equations used take in consideration the in-plane accelerations and the rotary inertia of the cross sections. Applying linear feedbacks, the authors obtain the exponential decay of the energy.