Global exponential stabilisation for the Burgers equation with localised control

2016/06/24 by Armen Shirikyan, Shirikyan, Armen · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1606.07752

openalex publication_date 2016/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the 1D viscous Burgers equation with a control localised in a finite interval. It is proved that, for any ε>0, one can find a time T of order logε^-1 such that any initial state can be steered to the ε-neighbourhood of a given trajectory at time T. This property combined with an earlier result on local exact controllability shows that the Burgers equation is globally exactly controllable to trajectories in a finite time. We also prove that the approximate controllability to arbitrary targets does not hold even if we allow infinite time of control.

Cited by

• Rapid boundary stabilization of 1D nonlinear parabolic equations
• Global exponential turnpike properties for optimal control of the viscous Burgers equation

Related

• Approximate controllability of the viscous Burgers equation on the real line
• Global exponential turnpike properties for optimal control of the viscous Burgers equation
• Global Exponential Stabilization for a Simplified Fluid-Particle Interaction System
• Finite-parameter feedback stabilization of original Burgers' equations\n and Burgers' equation with nonlocal nonlinearities
• On the local null controllability of a viscous Burgers' system in finite time