Infinite-Dimensional Dynamical Systems in Mechanics and Physics

This book presents dynamical systems in the infinite dimension, especially those generated by dissipative partial differential equations. This includes nonlinear parabolic equations such as reaction diffusion equations and Navier-Stokes equations; pattern formation equations such as Cahn-Hilliard and Kuramoto Sivashinsky equations; and wave equations such as the sine-Gordon equation, damped nonlinear wave equations, and weakly dissipative dispersive equations. The existence and uniqueness of solutions, the existence of a global attractor, and inertial manifolds when applicable are all studied in this book. In addition to a general revision of the book, two new topics have been added to this new edition: the study of the attractor (existence and regularity) in the absence of compactness; and the approximation of inertial manifolds by (convergent) families of smooth finite-dimensional manifolds and the approximation of attractors by (nonconvergent) sequences of similar manifolds. This book will be useful for researchers in mathematics, physics, and engineering.