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.
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.
Inhaltsverzeichnis
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.
