Related papers: Boundary null-controllability for the beam equatio…
This paper is concerned with the null controllability problem for a class of quasilinear parabolic equations under multiplicative control, locally supported in space. For the purpose of proving the existence of a multiplicative control…
We consider a $n \times n$ nonlinear reaction-diffusion system posed on a smooth bounded domain $\Omega$ of $\mathbb{R}^N$. This system models reversible chemical reactions. We act on the system through $m$ controls ($1 \leq m < n$),…
For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that control estimates give energy decay rates that explicitly depend…
We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when…
In this paper we prove existence and uniqueness results for nonlinear parabolic problems with Dirichlet boundary values whose model is \[ \left\{ \begin{aligned} &b(u)_t-\Delta_{p}u=\mu\;\mbox{in }(0,T)\times\Omega,\\…
This paper is concerned with the analysis of a one dimensional wave equation $z_{tt}-z_{xx}=0$ on $[0,1]$ with a Dirichlet condition at $x=0$ and a damping acting at $x=1$ which takes the form $(z_t(t,1),-z_x(t,1))\in\Sigma$ for every…
In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet…
Let the matrix operator $L = D\partial_{xx} + q(x)A_0$, with $D = diag(1, \nu)$, $\nu \neq 1$, $q \in L^{\infty} (0, $\pi$)$, and $A_0$ is a Jordan block of order 1. We analyze the boundary null controllability for system $y_t - Ly = 0$.…
This paper investigates the optimal control of a bilinear damped wave equation over an infinite time horizon. We establish the well-posedness of the controlled system and derive uniform energy estimates. The existence of optimal controls is…
In this paper we are interested on solvability of the problem \begin{align*} \begin{cases} -\Delta u=0 & \text{in} \;\;\;\mathbb{R}^{n+1}_{+}\;\;\;\;\;\;\;\;\;\\ \;\;\displaystyle{\frac{\partial u}{\partial \nu}} = V(x)u+b \vert…
In this paper, we study the small-time global null controllability of the generalized Burgers' equations $y_t + \gamma |y|^{\gamma-1}y_x-y_{xx}=u(t)$ on the segment $[0,1]$. The scalar control $u(t)$ is uniform in space and plays a role…
The local exact controllability of the one-dimensional bilinear Schr{\"o}dinger equation with Dirichlet boundary conditions has been extensively studied in subspaces of H 3 since the seminal work of K. Beauchard. Our first objective is to…
This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we address the well-posedness of the system by constructing an…
In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in…
In this paper, we study the null controllability of the three-dimensional Stokes equations with a memory term. For any positive final time $T>0$, we construct initial conditions such that the null controllability does not hold even if the…
In this manuscript we deal with regularity issues and the asymptotic behaviour (as $p \to \infty$) of solutions for elliptic free boundary problems of $p-$Laplacian type ($2 \leq p< \infty$): \begin{equation*} -\Delta_p u(x) +…
This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain of R^N (N>1) with coupling terms of zero and first orders and one control localized in some…
We study the boundary regularity of solutions to the porous medium equation $u_t = \Delta u^m$ in the degenerate range $m>1$. In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the…
One proves that the moving interface of a two-phase Stefan problem on $\ooo\subset\rr^d$, $d=1,2,3,$ is controllable at the end time $T$ by a Neumann boundary controller $u$. The phase-transition region is a mushy region $\{\sigma^u_t;\…
Let $(\Omega,g)$ be a piecewise-smooth, bounded convex domain in $\R^2$ and consider $L^2$-normalized Neumann eigenfunctions $\phi_{\lambda}$ with eigenvalue $\lambda^2$ and $u_{\lambda}:= \phi_{\lambda} |_{\partial \Omega}$ the associated…