Related papers: Approximate null-controllability with uniform cost…
We consider the typical one-dimensional strongly degenerate parabolic operator $Pu= u_t - (x^\alpha u_x)_x$ with $0<x<\ell$ and $\alpha\in(0,2)$, controlled either by a boundary control acting at $x=\ell$, or by a locally distributed…
In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control…
In this paper we study the exact controllability problem for the wave equation on a finite metric graph with the Kirchhoff-Neumann matching conditions. Among all vertices and edges we choose certain active vertices and edges, and give a…
Motivated by the modeling of the temporal structure of the velocity field in a highly turbulent flow, we propose and study a linear stochastic differential equation that involves the ingredients of a Ornstein-Uhlenbeck process, supplemented…
We study memory-type null controllability for linear parabolic equations with hereditary terms and time-dependent control regions. In contrast with classical null controllability, systems with memory require the simultaneous annihilation of…
We establish the null controllability for linear stochastic fourth order parabolic equations. Utilizing the duality argument, the null controllability is reduced to the observability for backward fourth order stochastic parabolic equations,…
We study several controllability properties for some semilinear parabolic PDE with a quadratic gradient term. For internal distributed controls, it is shown that the system is approximately and null controllable. The proof relies on the…
We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero,…
We obtain so far unproved properties of a ratio involving a class of Hermite and parabolic cylinder functions. Those ratios are shown to be strictly decreasing and bounded by universal constants. Differently to usual analytic approaches, we…
This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the…
In this paper, we examine the question of the boundary controllability of the one-dimensional non-isentropic Euler equation for compressible polytropic gas, in the context of weak entropy solutions. We consider the system in Eulerian…
We derive in a direct way the exact controllability of the 1D free Schr\"odinger equation with Dirichlet boundary control. We use the so-called flatness approach, which consists in parametrizing the solution and the control by the…
We consider the null-controllability problem for the generalized Baouendi-Grushin equation $(\partial_t - \partial_x^2 - q(x)^2\partial_y^2)f = 1_\omega u$ on a rectangular domain. Sharp controllability results already exist when the…
This article is devoted to analyze control properties for the heat equation with singular potential $-\mu/|x|^2$ arising at the boundary of a smooth domain $\Omega\subset \rr^N$, $N\geq 1$. This problem was firstly studied by Vancostenoble…
We establish a mixed observability inequality for a class of degenerate hyperbolic equations on the cylindrical domain $\Omega = \mathbb{T} \times (0,1)$ with mixed Neumann Dirichlet boundary conditions. The degeneracy acts only in the…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
We consider a transport equation by a gradient vector field with a small viscous perturbation --$\epsilon\Delta_g$. We study uniform observability (resp. controllability) properties in the (singular) vanishing viscosity limit…
This work is devoted to the control of the Fokker-Planck equation, posed on a smooth bounded domain of R^d, with a localized drift force. We prove that this equation is locally controllable to regular nonzero trajectories. Moreover, under…
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…
This article is concerned in the first place with the short-time observability constant of the heat equation from a subdomain $\omega$ of a bounded domain $M$. The constant is of the form $e^{\frac{K}{T}}$, where $K$ depends only on the…