Global attractors for von Karman evolutions with a nonlinear boundary dissipation.
type: Item
instance of: scholarly article
title: Global attractors for von Karman evolutions with a nonlinear boundary dissipation.
zbMATH Open document ID: 1041.37038
author: I. D. Chueshov
author: Irena Lasiecka
published in: Journal of Differential Equations
publication date: 2004-03-29T00:00:00Z
review text: The paper deals with a nonlinear system of dynamic elasticity described by the von Karman equation with a nonlinear boundary dissipation. The goal of the author is to obtain existence of a global attractor and to determine its structure. The authors prove finite dimensionality of a global attractor. Here they use a new approach to obtain finite fractal dimensionality of an attractor without using some differentiability of the corresponding semigroups. The ``infinite speed of propagation'' corresponding to the plate problems without rotational inertia play a crucial role in the authors' considerations. They conclude the paper by listing several open problems.
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 34D35
Mathematics Subject Classification ID: 74H40
zbMATH DE Number: 2062720
zbMATH Keywords: structure of attractors
zbMATH Keywords: finite fractal dimension
zbMATH Keywords: infinite speed of propagation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jde.2003.08.008
OpenAlex ID: W2014398079
cites work: A damped hyerbolic equation with critical exponent
cites work: Q4003101
cites work: Von Kármán's equations and the buckling of a thin elastic plate, II plate with general edge conditions
cites work: Uniqueness theorem for weak solutions of von Karman evolution equations
cites work: \(\alpha\)-contractions and attractors for dissipative semilinear hyperbolic equations and systems
cites work: FINITE DIMENSIONALITY OF AN ATTRACTOR IN SOME PROBLEMS OF NONLINEAR SHELL THEORY
cites work: STRONG SOLUTIONS AND THE ATTRACTOR OF THE VON KÁRMÁN EQUATIONS
cites work: On the Finiteness of the Number of Determining Elements for von Karman Evolution Equations
cites work: Introduction to the theory of infinite-dimensional dissipative systems. Transl. from the Russian by Constantin I. Chueshov, edited by Maryna B. Khorolska
cites work: ON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATION
cites work: Inertial manifolds for von Karman plate equations
cites work: Q5718853
cites work: Von Karman Evolution Equations
cites work: Finite dimensional exponential attractors for semilinear wave equations with damping
cites work: Global existence, uniqueness and regularity of solutions to a von Kármán system with nonlinear boundary dissipation
cites work: Q4033871
cites work: Global attractors for semilinear damped wave equations with supercritical exponent
cites work: Attractors for damped nonlinear hyperbolic equations
cites work: Q4039920
cites work: Q4948866
cites work: Uniform decay of weak solutions to a von Kármán plate with nonlinear boundary dissipation
cites work: Inverse problems for partial differential equations
cites work: Global existence of classical solutions to the dynamical von Kármán equations
cites work: Q4407522
cites work: Finite-dimensionality of bounded invariant sets for Navier-Stokes systems and other dissipative systems
cites work: Q3994379
cites work: Uniform stabilization of a nonlinear beam by nonlinear boundary feedback
cites work: Finite-dimensionality of attractors associated with von Kármán plate equations and boundary damping
cites work: Local and global compact attractors arising in nonlinear elasticity: The case of noncompact nonlinearity and nonlinear dissipation
cites work: Finite dimensionality and compactness of attractors for von Karman equations with nonlinear dissipation
cites work: Uniform decay rates for full von karman system of dynamic theromelasticity with free boundary conditions and partial boundary dissipation
cites work: Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
cites work: Sharp trace estimates of solutions to Kirchhoff and Euler-Bernoulli equations
cites work: Sharp regularity theory for elastic and thermoelastic Kirchhoff equations with free boundary conditions
cites work: Q5890172
cites work: Negatively invariant sets of compact maps and an extension of a theorem of Cartwright
cites work: On finite fractal dimension of the global attractor for the wave equation with nonlinear damping
cites work: Q4001083
cites work: Q4893982
cites work: Infinite-dimensional dynamical systems in mechanics and physics.
cites work: Q4169288
DOI: 10.1016/J.JDE.2003.08.008
description: scientific article; zbMATH DE number 2062720