Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation-Reference-Cited by-同舟云学术

Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation

Published:2019-02 Issue:02 Volume:29 Page:271-316
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Bastin Georges¹,Coron Jean-Michel²³,Hayat Amaury²⁴,Shang Peipei²⁴⁵

Affiliation:

1. Department of Mathematical Engineering, ICTEAM, University of Louvain, Louvain-La-Neuve 1348, Belgium

2. Sorbonne Université, UPMC Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France

3. Institute for Theoretical Studies (ITS), Eidgenössische Technische Hochschule Zürich, Zürich 8092, Switzerland

4. Forschungsinstitut für Mathematik (FIM), Eidgenössische Technische Hochschule Zürich, Zürich 8092, Switzerland

5. School of Mathematical Sciences, Tongji University, Shanghai, 200092, P. R. China

Abstract

In this paper, we study the exponential stabilization of a shock steady state for the inviscid Burgers equation on a bounded interval. Our analysis relies on the construction of an explicit strict control Lyapunov function. We prove that by appropriately choosing the feedback boundary conditions, we can stabilize the state as well as the shock location to the desired steady state in [Formula: see text]-norm, with an arbitrary decay rate.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021820251950009X

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1. On the Attainable Set for Scalar Nonlinear Conservation Laws with Boundary Control

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