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Von Karman Evolution Equations
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Von Karman Evolution Equations

Well-posedness and Long Time Dynamics
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Igor Chueshov
1267 g
242x167x51 mm
Schriftenreihe Markt und Marketing Springer Monographs in Mathematics

This book presents results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. The coverage is comprehensive and elf-contained, and the theory applies to many similar dynamics.
Authors well-known experts of nonlinear PDEExhaustive introduction in theory and methods of evolutionary Karman plate theory
Self-contained exposition of methods pertaining to well-posedness, stability
Critical nonlinearities and nonlinear damping highly exposed
Relevant tools developed. These constitute new and original results in the field
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 Wave-Plate Systems.- Inertial Manifolds for von Karman Plate Equations.
In the study of mathematical models that arise in the context of concrete - plications, the following two questions are of fundamental importance: (i) we- posedness of the model, including existence and uniqueness of solutions; and (ii) qualitative properties of solutions. A positive answer to the ?rst question, - ing of prime interest on purely mathematical grounds, also provides an important test of the viability of the model as a description of a given physical phenomenon. An answer or insight to the second question provides a wealth of information about the model, hence about the process it describes. Of particular interest are questions related to long-time behavior of solutions. Such an evolution property cannot be v- i?ed empirically, thus any in a-priori information about the long-time asymptotics can be used in predicting an ultimate long-time response and dynamical behavior of solutions. In recent years, this set of investigations has attracted a great deal of attention. Consequent efforts have then resulted in the creation and infusion of new methods and new tools that have been responsible for carrying out a successful an- ysis of long-time behavior of several classes of nonlinear PDEs.

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