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Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping
Igor Chueshov, Kharkov University, Ukraine, and Irena Lasiecka, University of Virginia, Charlottesville, VA

Memoirs of the American Mathematical Society
2008; 183 pp; softcover
Volume: 195
ISBN-10: 0-8218-4187-4
ISBN-13: 978-0-8218-4187-7
List Price: US$80
Individual Members: US$48
Institutional Members: US$64
Order Code: MEMO/195/912
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The authors consider abstract nonlinear second order evolution equations with a nonlinear damping. Questions related to long time behavior, existence and structure of global attractors are studied. Particular emphasis is put on dynamics which--in addition to nonlinear dissipation-- have noncompact semilinear terms and whose energy may not be necessarily decreasing. For such systems the authors first develop a general theory at the abstract level. They then apply the general theory to nonlinear wave and plate equations exhibiting the aforementioned characteristics and are able to provide new results pertaining to several open problems in the area of structure and properties of global attractors arising in this class of PDE dynamics.

Table of Contents

  • Introduction
  • Abstract results on global attractors
  • Existence of compact global attractors for evolutions of the second order in time
  • Properties of global attractors for evolutions of the second order in time
  • Semilinear wave equation with a nonlinear dissipation
  • Von Karman evolutions with a nonlinear dissipation
  • Other models from continuum mechanics
  • Bibliography
  • Index
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