Evolution equations and their trajectory attractors
نویسندگان
چکیده
منابع مشابه
Trajectory and global attractors for evolution equations with memory
Our aim in this note is to analyze the relation between two notions of attractors for the study of the long time behavior of equations with memory, namely the so-called past history approach and a more recent one based on the notion of a trajectory attractor. 2000 Mathematics Subject Classification. 35B41, 37L30, 45K05.
متن کاملAttractors of partial differential evolution equations and estimates of their dimension
CONTENTS Introduction 151 § 1. Maximal attractors of semigroups generated by evolution equations 156 § 2. Examples of parabolic equations and systems having a maximal attractor 158 § 3. The Hausdorff dimension of invariant sets 164 § 4. Estimate of the change in volume under the action of shift operators generated by linear evolution equations 167 § 5. An upper bound for the Hausdorff dimension...
متن کاملAttractors for Parametric Delay Differential Equations and their Continuous Behavior
The problem of the continuity of global attractors under minimal assumptions for a general class of parameterized delay differential equations is considered. The theory of equi-attraction developed by Li and Kloeden in [Li & Kloeden, 2004a] is adapted to this framework, so it is proved that the continuity of the attractors with respect to the parameter is equivalent to this equi-attraction prop...
متن کاملTrajectory and smooth attractors for Cahn-Hilliard equations with inertial term
The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient ε > 0 which is usually small in comparison to the other physical constants. The main feature of this equation is the fact that even a globally bounded nonlineari...
متن کاملTrajectory and global attractors of the boundary value problem for motion equations of viscoelastic medium
Attractors for systems of differential equations or for dynamical systems are the sets to which the solutions of an equation or trajectories of a system are eventually attracted (after damping of transient processes). As a rule, to the condition of attraction one adds the conditions of strict invariance, minimality and compactness. The classical examples of attractors are equilibrium points or ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 1997
ISSN: 0021-7824
DOI: 10.1016/s0021-7824(97)89978-3