Related papers: Exact controllability and stabilization for linear…
We present a mathematical and numerical analysis on a control model for the time evolution of a multi-layered piezoelectric cantilever with tip mass and moment of inertia, as developed by Kugi and Thull [31]. This closed-loop control system…
Rapidly decreasing tempered stable distributions are useful models for financial applications. However, there has been no exact method for simulation available in the literature. We remedy this by introducing an exact simulation method in…
We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard finite element…
In a companion paper [Pitrou, Phys. Rev. E 97, 043115 (2018)], a formalism allowing to describe viscous fibers as one-dimensional objects was developed. We apply it to the special case of a viscous fluid torus. This allows to highlight the…
The goal of this article is to present a local exact controllability result for the 2 and 3-dimensional compressible Navier-Stokes equations on a constant target trajectory when the controls act on the whole boundary. Our study is then…
This work is concerned with the necessary conditions of optimality for a minimal time control problem $(P)$ for the linearized Navier-Stokes periodic flow in a 2D-channel, subject to a boundary input which acts on the transversal component…
We study well-posedness, stabilization and control problems involving freely vibrating beams that may undergo motions of large magnitude -- i.e. large displacements of the reference line and large rotations of the cross sections. Such…
This paper is concerned with the control properties of the Korteweg-de Vries (KdV) equation posed on a bounded interval with a distributed control. When the control region is an arbitrary open subdomain, we prove the null controllability of…
The paper is devoted to studying controllability properties for 3D Navier-Stokes equations in a bounded domain. We establish a sufficient condition under which the problem in question is exactly controllable in any finite-dimensional…
We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in $H^{-1}(\mathbb{R})$. By comparison, the optimal regularity for well-posedness on the torus is known to be…
Boundary controllers have been recently proposed in the literature, via modal decomposition, to achieve $H^1$ stabilization of linear parabolic equations in two and three dimensions. In one dimension ($1$-D), $H^1$ exponential stability is…
This paper is the first part of a work which consists in proving the stabilization to zero of a fluid-solid system, in dimension 2 and 3. The considered system couples a deformable solid and a viscous incompressible fluid which satisfies…
We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the…
In this paper we study controllability of a linear equation with persistent memory when the control belongs to $ H^k_0(0,T;L^2(\ZOMq)) $. In the case the memory is zero, our equation is reduced to the wave equation and a result due to…
In this paper, we consider the problem of second moment stabilization of a scalar linear plant with process noise. We assume that the sensor must communicate with the controller over an unreliable channel, whose state evolves according to a…
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity…
In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous…
Considering a wave-reaction-diffusion PDE cascade system with wave Neumann control, we first establish controllability properties in a suitable Hilbert space depending on the coupling cascade term. This is done by deriving an observability…
It is shown that a switching control involving a finite number of Dirac delta actuators is able to steer the state of a general class of nonautonomous parabolic equations to zero as time increases to infinity. The strategy is based on a…
We derive new results regarding the controllability and the reachability of multitime controlled linear PDE systems of first order. These systems describe some important multitime evolution in engineering, economics and biology. Some of…