Long Time Behavior Of Second Order Evolution Equations With Nonlinear Damping
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Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping
Author: Igor Chueshov
language: en
Publisher: American Mathematical Soc.
Release Date: 2008
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 theoryto 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.
Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping
Author: I. Lasiecka, Igor Chueshov
language: en
Publisher: American Mathematical Soc.
Release Date: 2008-08-08
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.
Moderate Deviations for the Range of Planar Random Walks
Author: Richard F. Bass
language: en
Publisher: American Mathematical Soc.
Release Date: 2009-03-06
Given a symmetric random walk in ${\mathbb Z}^2$ with finite second moments, let $R_n$ be the range of the random walk up to time $n$. The authors study moderate deviations for $R_n -{\mathbb E}R_n$ and ${\mathbb E}R_n -R_n$. They also derive the corresponding laws of the iterated logarithm.