GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS-Reference-Cited by-同舟云学术

GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS

Published:2006-08 Issue:04 Volume:08 Page:535-567
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

CORON JEAN-MICHEL¹,TRÉLAT EMMANUEL²

Affiliation:

1. Institut Universitaire de France et Université Paris-Sud, Département de Mathématique, 91405 Orsay Cedex, France

2. Université Paris-Sud, Département de Mathématique, 91405 Orsay Cedex, France

Abstract

This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steady-state to any other one by means of a boundary control, provided that they are in the same connected component of the set of steady-states. The proof is based on an expansion of the solution in a one-parameter Riesz basis of generalized eigenvectors, and on an effective feedback stabilization procedure which is implemented.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199706002209

Reference28 articles.

1. Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary

2. Local controllability of a 1-D Schrödinger equation

3. Controllability of a quantum particle in a moving potential well

4. Well posedness and control of semilinear wave equations with iterated logarithms

Cited by 54 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Observer-Based Feedback-Control for the Stabilization of a Class of Parabolic Systems;Journal of Optimization Theory and Applications;2024-08-08

2. On the Exact Boundary Controllability of Semilinear Wave Equations;SIAM Journal on Control and Optimization;2024-07-03

3. Quantitative Rapid and Finite Time Stabilization of the Heat Equation;ESAIM: Control, Optimisation and Calculus of Variations;2024

4. Local Exponential Stabilization of Rogers–McCulloch and FitzHugh–Nagumo Equations by the Method of Backstepping;ESAIM: Control, Optimisation and Calculus of Variations;2024

5. Linear Control Systems in Banach Spaces;SpringerBriefs on PDEs and Data Science;2024