Memoirs of the American Mathematical Society 2008; 183 pp; softcover Volume: 195 ISBN10: 0821841874 ISBN13: 9780821841877 List Price: US$76 Individual Members: US$45.60 Institutional Members: US$60.80 Order Code: MEMO/195/912
 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 whichin 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
