Infinite-dimensional dynamical systems in mechanics and physics
By: Roger Temam.
Edition: 2nd ed.
Series: Applied mathematical sciences ;; 68; Applied mathematical sciences (Springer-Verlag New York Inc.) ;; v. 68.
Publisher: Springer
Published: 1997
Place of publication: New York
Language: eng
Number of pages: 648
Subjects: Differentiable dynamical systems; Boundary value problems; Nonlinear theories
Description: 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.
Notes: Includes bibliographical references (p. [613]-643) and index.