Von Karman Evolution Equations
Well-posedness and Long Time Dynamics
Chueshov, Igor.
creator
author.
Lasiecka, Irena.
author.
SpringerLink (Online service)
text
xxu
2010
monographic
eng
access
XIV, 770 p. 10 illus. online resource.
The main goal of this book is to discuss and present results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. While many of the results presented here are the outgrowth of very recent studies by the authors, including a number of new original results here in print for the first time authors have provided a comprehensive and reasonably self-contained exposition of the general topic outlined above. This includes supplying all the functional analytic framework along with the function space theory as pertinent in the study of nonlinear plate models and more generally second order in time abstract evolution equations. While von Karman evolutions are the object under considerations, the methods developed transcendent this specific model and may be applied to many other equations, systems which exhibit similar hyperbolic or ultra-hyperbolic behavior (e.g. Berger's plate equations, Mindlin-Timoschenko systems, Kirchhoff-Boussinesq equations etc). In order to achieve a reasonable level of generality, the theoretical tools presented in the book are fairly abstract and tuned to general classes of second-order (in time) evolution equations, which are defined on abstract Banach spaces. The mathematical machinery needed to establish well-posedness of these dynamical systems, their regularity and long-time behavior is developed at the abstract level, where the needed hypotheses are axiomatized. This approach allows to look at von Karman evolutions as just one of the examples of a much broader class of evolutions. The generality of the approach and techniques developed are applicable (as shown in the book) to many other dynamics sharing certain rather general properties. Extensive background material provided in the monograph and self-contained presentation make this book suitable as a graduate textbook.
Well-Posedness -- Preliminaries -- Evolutionary Equations -- Von Karman Models with Rotational Forces -- Von Karman Equations Without Rotational Inertia -- Thermoelastic Plates -- Structural Acoustic Problems and Plates in a Potential Flow of Gas -- Long-Time Dynamics -- Attractors for Evolutionary Equations -- Long-Time Behavior of Second-Order Abstract Equations -- Plates with Internal Damping -- Plates with Boundary Damping -- Thermoelasticity -- Composite Waveâ€“Plate Systems -- Inertial Manifolds for von Karman Plate Equations.
by Igor Chueshov, Irena Lasiecka.
Mathematics
Mathematical analysis
Analysis (Mathematics)
Dynamics
Ergodic theory
Partial differential equations
Applied mathematics
Engineering mathematics
Mathematics
Partial Differential Equations
Dynamical Systems and Ergodic Theory
Analysis
Applications of Mathematics
QA370-380
515.353
Springer eBooks
Springer Monographs in Mathematics
9780387877129
http://dx.doi.org/10.1007/978-0-387-87712-9
http://dx.doi.org/10.1007/978-0-387-87712-9
100427
20180115171426.0
978-0-387-87712-9