000 04184nam a22005055i 4500
001 978-0-387-87712-9
003 DE-He213
005 20140220084456.0
007 cr nn 008mamaa
008 100427s2010 xxu| s |||| 0|eng d
020 _a9780387877129
_9978-0-387-87712-9
024 7 _a10.1007/978-0-387-87712-9
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aChueshov, Igor.
_eauthor.
245 1 0 _aVon Karman Evolution Equations
_h[electronic resource] :
_bWell-posedness and Long Time Dynamics /
_cby Igor Chueshov, Irena Lasiecka.
264 1 _aNew York, NY :
_bSpringer New York,
_c2010.
300 _aXIV, 778p. 10 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _aWell-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 Wave–Plate Systems -- Inertial Manifolds for von Karman Plate Equations.
520 _aThe 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.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aDifferentiable dynamical systems.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aAnalysis.
650 2 4 _aApplications of Mathematics.
700 1 _aLasiecka, Irena.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387877112
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-87712-9
912 _aZDB-2-SMA
999 _c109837
_d109837