Von Karman Evolution Equations: Well-posedness and Long Time Dynamics (Springer Monographs in Mathematics)

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.

Lasiecka, Irena

Chueshov, Igor

Reference

Springer

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.

The main goal of this book is to systematically address the mathematical methods that are applied in the study of synchronization of infinite-dimensional evolutionary dissipative or partially dissipative systems. It bases its unique monograph presentation on both general and abstract models and covers several important classes of coupled nonlinear deterministic and stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts readily to advanced graduate coursework in dissipative dynamics, requires some background knowledge in evolutionary equations and introductory functional analysis as well as a basic understanding of PDEs and the theory of random processes. Suitable for researchers in synchronization theory, the book is also relevant to physicists and engineers interested in both the mathematical background and the methods for the asymptotic analysis of coupled infinite-dimensional dissipative systems that arise in continuum mechanics.

Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems (Applied Mathematical Sciences, 204)

Schmalfuß, Björn

Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems (Applied Mathematical Sciences)

This book is devoted to background material and recently developed mathematical methods in the study of infinite-dimensional dissipative systems. The theory of such systems is motivated by the long-term goal to establish rigorous mathematical models for turbulent and chaotic phenomena. The aim here is to offer general methods and abstract results pertaining to fundamental dynamical systems properties related to dissipative long-time behavior. The book systematically presents, develops and uses the quasi-stability method while substantially extending it by including for consideration new classes of models and PDE systems arising in Continuum Mechanics. The book can be used as a textbook in dissipative dynamics at the graduate level.
Igor Chueshov is a Professor of Mathematics at Karazin Kharkov National University in Kharkov, Ukraine.

Dynamics of Quasi-Stable Dissipative Systems (Universitext)

The aim of this book is to present a recently developed approach suitable for investigating a variety of qualitative aspects of order-preserving random dynamical systems and to give the background for further development of the theory. The main objects considered are equilibria and attractors. The effectiveness of this approach is demonstrated by analysing the long-time behaviour of some classes of random and stochastic ordinary differential equations which arise in many applications.

Monotone Random Systems Theory and Applications (Lecture Notes in Mathematics, 1779)

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Books by Chueshov, Igor

See the best price to sell, buy, or rent books by Chueshov, Igor. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Von Karman Evolution Equations: Well-posedness and Long Time Dynamics (Springer Monographs in Mathematics)

Von Karman Evolution Equations: Well-posedness and Long Time Dynamics (Springer Monographs in Mathematics)

Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems (Applied Mathematical Sciences, 204)

Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems (Applied Mathematical Sciences)

Dynamics of Quasi-Stable Dissipative Systems (Universitext)

Monotone Random Systems Theory and Applications (Lecture Notes in Mathematics, 1779)