Related papers: On the control of the Burgers-alpha model
This work is devoted to prove the global uniform exact controllability of the inviscid and viscous Burgers-$\alpha$ systems. The state $y$ is the solution to a regularized Burgers equation, where the transport velocity $z$ consists of a…
This paper is devoted to study the controllability of a one-dimensional fluid-particle interaction model where the fluid follows the viscous Burgers equation and the point mass obeys Newton's second law. We prove the null controllability…
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…
We consider the 1D viscous Burgers equation with a control localised in a finite interval. It is proved that, for any $\varepsilon>0$, one can find a time $T$ of order $\log\varepsilon^{-1}$ such that any initial state can be steered to the…
We consider the one-dimensional Burgers' equation linearized at a stationary shock, and investigate its null-controllability cost with a control at the left endpoint. We give an upper and a lower bound on the control time required for this…
The paper is devoted to studying the 1D viscous Burgers equation controlled by an external force. It is assumed that the initial state is essentially bounded, with no decay condition at infinity, and the control is a trigonometric…
This paper is devoted to the local null controllability of the Burgers control system $y_t - y_{xx} + y y_x = u(t)$ on a bounded interval imposed by the zero Dirichlet boundary condition. It is known from the work of Marbach that this…
This paper deals with the distributed and boundary controllability of the so called Leray-$\alpha$ model. This is a regularized variant of the Navier-Stokes system ($\alpha$ is a small positive parameter) that can also be viewed as a model…
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…
In this work, we are interested in the small time local null controllability for the viscous Burgers' equation $y_t - y_{xx} + y y_x = u(t)$ on the line segment $[0,1]$, with null boundary conditions. The second-hand side is a scalar…
We study the problem of global exponential stabilization of original Burgers' equations and the Burgers' equation with nonlocal nonlinearities by controllers depending on finitely many parameters. It is shown that solutions of the…
We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…
In this paper, we consider forward stochastic nonlinear parabolic equations, with a control localized in the drift term. Under suitable assumptions, we prove the small-time global null-controllability, with a truncated nonlinearity. We also…
In this work, we are interested in the small time global null controllability for the viscous Burgers' equation y_t - y_xx + y y_x = u(t) on the line segment [0,1]. The second-hand side is a scalar control playing a role similar to that of…
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions to Burgers'…
We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set $\omega$. We prove…
We explore a connection of the forced Burgers equation with the Schr\"{o}dinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions that allow to…
Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers'…
This paper deals with the control of a kind of turbulent flows. We consider a simplified k-e model with distributed controls, locally supported in space. We proof that the system is partially locally null-controllable, in the sense that the…