Related papers: Null Controllability for a Multi-Dimensional Degen…
In this paper, we consider a parabolic PDE on a torus of arbitrary dimension. The nonlinear term is a smooth function of polynomial growth of any degree. In this general setting, the corresponding Cauchy problem is not necessarily well…
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…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…
This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…
Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…
We explore how the analysis of the Carleman linearization can be extended to dynamical systems on infinite-dimensional Hilbert spaces with quadratic nonlinearities. We demonstrate the well-posedness and convergence of the truncated Carleman…
We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove…
The main purpose of this paper is to apply the notion of hierarchical control to a coupled degenerate non linear parabolic equations. We use the Stackelberg-Nash strategy with one leader and two followers. The followers solve a Nash…
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order model, such as a deep neural network, to approximate the…
We prove the internal controllability of some systems of two coupled wave equations in one space dimension, with one control, under certain conditions on the coupling. To do this we apply the "fictitious control method" in two cases:…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
We establish the internal exact controllability of a refined stochastic hyperbolic equation by deriving a suitable observability inequality via Carleman estimates for the associated backward stochastic hyperbolic equation. In contrast to…
In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient…
The aim of this work is to consider the controllability problem of the linear system associated to Korteweg-de Vries Burgers equation posed in the whole real line. We obtain a sort of exact controllability for solutions in $L^2_{loc}(\R^2)$…
We investigate a backward anisotropic stochastic parabolic equation with general dynamic boundary conditions, where the drift involves both $\mathbb{L}^2$ and $\mathbb{H}^{-1}$ bulk--surface terms. We first establish the well-posedness of…
Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi)$. The null controllability properties of the equation $$u_{tt}+\Delta^2 u+\rho (\Delta)^\alpha u_t=F(x,t)$$ are studied. Let $T>0$, and assume initial conditions $(u^0,u^1)\in…
We study the minimum energy null-controllability problem for differential equations with point-wise delays. For the equations of both neutral and retarded type we reduce the problem of finding the optimal control to a Volterra integral…
In this paper, a quasi-linear parabolic equation with a diffusion term dependent on the gradient to the state with Dirichlet boundary conditions is considered. The goal of this paper is to prove the existence of control that insensitizes…
In this paper, we deal with the existence of insensitizing controls for the Navier-Stokes equations in a bounded domain with Dirichlet boundary conditions. We prove that there exist controls insensitizing the $L^2$ -norm of the observation…
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…