# Global Controllability of Nonviscous and Viscous Burgers-Type Equations

@article{Chapouly2009GlobalCO,
title={Global Controllability of Nonviscous and Viscous Burgers-Type Equations},
author={Marianne Chapouly},
journal={SIAM J. Control. Optim.},
year={2009},
volume={48},
pages={1567-1599}
}
In this paper, we deal with both nonviscous and viscous Burgers-type equations on a bounded interval. We study the global exact controllability of these equations when we have three controls: one control is the right member of the equation and is constant with respect to the space variable; the two others are the boundary values. For a first time, we are interested in nonviscous Burgers-type equations and we prove their global exact controllability for every time $T>0$ with such controls thanks…
43 Citations

## Figures from this paper

### On the uniform controllability for a family of non-viscous and viscous Burgers-α systems

• Mathematics
ESAIM: Control, Optimisation and Calculus of Variations
• 2021
In this paper we study the global controllability of families of the so called non-viscous and viscous Burgers-α systems by using boundary and space independent distributed controls. In these

### Approximate controllability of the viscous Burgers equation on the real line

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

### GLOBAL CONTROLLABILITY OF A NONLINEAR KORTEWEG–DE VRIES EQUATION

We are interested in both the global exact controllability to the trajectories and in the global exact controllability of a nonlinear Korteweg–de Vries equation in a bounded interval. The local exact

### Remarks on global controllability for the shallow-water system with two control forces

• Mathematics
• 2012
In this paper we deal with the compressible Navier-Stokes equations with a friction term in one dimension on an interval. We study the exact controllability properties of this equation with general

### Small-time global null controllability of generalized Burgers' equations

In this paper, we study the small-time global null controllability of the generalized Burgers’ equations y t + ( | y | γ ) x − y xx = u ( t ) on the segment [0 , 1]. The scalar control u ( t ) is

### Global exponential stabilisation for the Burgers equation with localised control

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

### Uniform Controllability of Scalar Conservation Laws in the Vanishing Viscosity Limit

This work constructs boundary controls so that the solution is driven to the targeted constant state, and requires these controls to be uniformly bounded as $\varepsilon \rightarrow 0^+$ in an appropriate space.

## References

SHOWING 1-10 OF 22 REFERENCES

### On the Uniform Controllability of the Burgers Equation

• Mathematics
SIAM J. Control. Optim.
• 2007
The (global) exact controllability property to nonzero constant states is proved with control functions whose norms in an appropriate space are bounded independently of $\nu$, which belongs to a suitably small interval.

### Obstruction and some approximate controllability results for the burgers equation and related problems

The paper studies the approximate controllability for the Burgers equation. Due to the presence of a superlinear term, an obstruction phenomenon arises which implies a lack of approximate

### On Controllability of Certain Systems Simulating a Fluid Flow

• Mathematics
• 1995
Approximate controllability of the Stokes system is established by a constructive method when control is a right-hand-side concentrated in subdomain i.e. in the case of local distributed control.

### On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions

For boundary or distributed controls, we get an approximate controllability result for the Navier-Stokes equations in dimension 2 in the case where the fluid is incompressible and slips on the

### Control and Nonlinearity

This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to

### Exact Boundary Controllability for Quasi-Linear Hyperbolic Systems

• Mathematics
SIAM J. Control. Optim.
• 2003
The exact boundary controllability for quasi-linear hyperbolic systems if the C1 norm of initial and final states is small enough is established.

### Exact boundary controllability of 3-D Euler equation

We prove the exact boundary controllability of the 3-D Euler equation of incompressible inviscid fluids on a regular connected bounded open set when the control operates on an open part of the

### On the controllability of the burger equation

We present here a return method to describe some attainable sets on an interval of the classical Burger equation by means of the variation of the domain.