On a class of nonlinear distributed systems with linear finite dimensional feedback controls
type: Item
instance of: scholarly article
title: On a class of nonlinear distributed systems with linear finite dimensional feedback controls
zbMATH Open document ID: 0594.93040
DOI: 10.1016/0022-247X(86)90097-1
author: P. K. C. Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The author studies certain asymptotic properties of nonlinear distributed parameter systems in the presence of linear finite dimensional feedback controls. He considers dynamical systems described by a class of nonlinear evolution equations in a Hilbert space, which includes the Navier-Stokes equations and the magnetohydrodynamic equations with homogeneous boundary conditions. He shows that linear feedback controls depending on a finite number of modes assure that for bounded solutions of the system, their asymptotic behavior as \(t\to \infty\) is completely determined by that of a corresponding finite number of modes, that is, the bounded solutions of the system tend to an invariant set having a finite dimensional structure as \(t\to \infty\).
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35B37
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 3956923
zbMATH Keywords: nonlinear distributed parameter systems
zbMATH Keywords: linear finite dimensional feedback controls
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: magnetohydrodynamic equations
reviewed by: Toshihiro Kobayashi
MaRDI profile type: Publication
cites work: Q3931212
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cites work: Energy conserving Galerkin approximations for 2-D hydrodynamic and MHD Bénard convection
full work available at URL: 0022-247x(86)90097-1
OpenAlex ID: W2069128957
description: scientific article; zbMATH DE number 3956923