Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems

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.

Addresses several important classes of nonlinear PDEs Adapts as a textbook for advanced graduate courses in dissipative dynamics Appeals to both mathematicians interested in synchronization theory as well as physicists and engineers interested in mathematical background and methods for the asymptotic analysis of infinite-dimensional dissipative systems Uniquely presents synchronization theory in the infinite-dimensional case at the monograph level Remains accessible to advanced students and scientific professionals without deep knowledge of Sobolev theory and functional spaces

Résumé
"The book ends with full references and an index. The book is a self-contained piece ... ." (Yilun Shang, Mathematical Reviews, March, 2022)

Contenu
Introduction.- Part I: Deterministic Systems.- Synchronization of global attractors and individual trajectories.- Master-slave synchronization via invariant manifolds.- Part II: Stochastic Systems.- Stochastic Synchronization of Random Pullback Attractors.- Master-slave synchronization in random systems.