A01=Albert J. Milani
A01=Norbert J. Koksch
absorbing
absorbing sets
advanced dynamical systems theory
asymptotic stability
attractor
Author_Albert J. Milani
Author_Norbert J. Koksch
Autonomous Ode
Backward Orbit
Banach Space
Bernoulli's Sequences
Bernoulli’s Sequences
Bounded Subsets
Category=PBKJ
Category=PBW
Category=PHU
cauchy
Cauchy Problem
Complete Orbit
continuous semiflows
differential evolution equation
Duffing's Equation
Duffing’s Equation
dynamical systems
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eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
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exponential
EXPONENTIAL ATTRACTOR
Finite Dimensional
Finite Dimensional Dynamical Systems
Fixed Point
Forward Orbit
functional analysis
global
Global Attractor
inertial
Inertial Manifolds
Long Time Behavior
manifold
mathematical modeling
nonlinear analysis
partial differential equations
positive
Positively Invariant
problem
set
Stroboscopic Map
Totally Bounded
Unstable Manifold
Product details
- ISBN 9780367454289
- Weight: 544g
- Dimensions: 152 x 229mm
- Publication Date: 25 Nov 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the asymptotic behavior of the solutions of DEEs. The authors concentrate on three types of absorbing sets: attractors, exponential attractors, and inertial manifolds. They present the fundamental properties of these sets, and then proceed to show the existence of some of these sets for a number of dynamical systems generated by well-known physical models. In particular, they consider in full detail two particular PDEEs: a semilinear version of the heat equation and a corresponding version of the dissipative wave equation. These examples illustrate the most important features of the theory of semiflows and provide a sort of template that can be applied to the analysis of other models.
The material builds in a careful, gradual progression, developing the background needed by newcomers to the field, and culminating in a more detailed presentation of the main topics than found in most sources. The authors' approach to and treatment of the subject builds the foundation for more advanced references and research on global attractors, exponential attractors, and inertial manifolds.
Albert J. Milani is a professor in the Department of Mathematics, University of Wisconsin-Milwaukee, USA.
Norbert J. Koksch is a docent in the Department of Mathematics, Technische Universität, Dresden, Germany
