Related papers: Null controllability of some degenerate wave equat…
Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find a unified framework that encompasses and generalizes the…
We propose a numerical method to approximate the exact averaged boundary control of a family of wave equations depending on an unknown parameter sigma. More precisely the control, independent of sigma, that drives an initial data to a…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi)$, and let $T>0$. We prove a well-posedness results for the structurally damped beam equation $$u_{tt}+\Delta^2 u-\rho \Delta u_t=0, x\in (0,\pi),t>0$$ with various boundary…
In this paper we introduce a method to find the minimal control time for the null controllability of 1D first-order linear hyperbolic systems by one-sided boundary controls when the coefficients are regular enough.
We consider nxn hyperbolic systems of balance laws in one-space dimension under the assumption that all negative (resp. positive) characteristics are linearly degenerate. We prove the local exact one-sided boundary null controllability of…
We consider the large time behavior of solutions to the following nonlinear wave equation: $\partial_{t}^2 u = c(u)^{2}\partial^2_x u + \lambda c(u)c'(u)(\partial_x u)^2$ with the parameter $\lambda \in [0,2]$. If $c(u(0,x))$ is bounded…
This paper addresses null controllability for both forward and backward linear stochastic parabolic equations by introducing convection terms on the drift parts with bounded coefficients. Moreover, the forward stochastic parabolic equation…
The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an…
We study a control problem governed by a semilinear parabolic equation. The control is a measure that acts as the kernel of a possibly nonlocal time delay term and the functional includes a non-differentiable term with the measure-norm of…
In this paper, we study the simultaneous controllability of wave systems in an open domain of R d , d $\in$ N *. We obtain a partial controllability result on a co-finite dimensional space for wave equations coupled by a single control…
A widely used stochastic wave equation is the classical wave equation perturbed by a term of It\^o's integral. We show that this equation is not exactly controllable even if the controls are effective everywhere in both the drift and the…
Sufficient and necessary conditions are established for controllability of affine control systems where the control is constrained to a set whose convex hull contains the origin but is not necessarily, in contrast with previously known…
In this paper, we establish some important results for the impulsive wave equation. We begin by proving the existence of a solution. Then, we study the impulse approximate controllability where the control function acts on a subdomain…
The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous…
This paper extends our previous controllability results for a class of coupled linear parabolic systems with nonlocal interactions, motivated by applications in finance such as generalized Black--Scholes models. We establish local null…
We give a boundary observability result for a $1$d wave equation with a potential. We then deduce with a Schauder fixed-point argument the existence of a Neumann boundary control for a semi-linear wave equation $\partial_{tt}y -…
This paper addresses the output regulation problem for a one-dimensional unstable wave equation subject to output delay and all-channel disturbances with unknown frequencies and amplitudes. First, this problem is transformed into a…