Global exact controllability of a class of quasilinear hyperbolic systems
type: Item
instance of: scholarly article
title: Global exact controllability of a class of quasilinear hyperbolic systems
zbMATH Open document ID: 0915.93007
author: Bing-Yu Zhang
author: Tatsien Li
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-02-17T00:00:00Z
review text: This paper treats a distributed parameter boundary control system described by a reducible quasilinear hyperbolic system \[ {\partial r\over\partial t}+\lambda(r,s) {\partial r\over\partial x}=0 \] \[ {\partial s \over\partial t}+ \mu(r,s){\partial s\over \partial x}=0, \quad x\in [0,1], \] (where \(\lambda(r,s) <0<\mu(r,s))\) with the nonlinear boundary conditions \[ s=g (r,t)+h_1(t)\text{ at }x=0 \] \[ r=f(s,t)+h_2(t)\text{ at }x=1. \] It is shown that the system is globally exactly boundary controllable in the linear degenerate case.
reviewed by: Sebastian Aniţa
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1218648
zbMATH Keywords: global exact controllability
zbMATH Keywords: distributed parameter boundary control system
zbMATH Keywords: reducible quasilinear hyperbolic system
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6037
OpenAlex ID: W2018076730
cites work: Energie decay estimates and exact boundary value controllability for the wave equation in a bounded domain
cites work: Controllability of the Nonlinear Wave Equation in Several Space Variables
cites work: Nonlinear hyperbolic problems with solutions on preassigned sets
cites work: Boundary Controllability of Nonlinear Hyperbolic Systems
cites work: Local controllability of a nonlinear wave equation
cites work: Q3732154
cites work: Q3752171
cites work: Decay of solutions of wave equations in a bounded region with boundary dissipation
cites work: Uniform exponential energy decay of wave equations in a bounded region with \(L_ 2(0,\infty;L_ 2(\Gamma))\)-feedback control in the Dirichlet boundary conditions
cites work: Exact controllability of the wave equation with Neumann boundary control
cites work: Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems
cites work: Hyperbolic systems of conservation laws II
cites work: Q3762928
cites work: Q4852353
cites work: Exact Controllability, Stabilization and Perturbations for Distributed Systems
cites work: Q3658380
cites work: Q5617182
cites work: Boundary Value Control of the Higher-Dimensional Wave Equation
cites work: Control theory of hyperbolic equations related to certain questions in harmonic analysis and spectral theory
cites work: Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions
cites work: Exact controllability and stabilizability of the Korteweg-de Vries equation
cites work: Q3832966
cites work: Exact controllability for the semilinear wave equation
cites work: Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping
DOI: 10.1006/JMAA.1998.6037
description: scientific article; zbMATH DE number 1218648