Nonlinear Pdes: A Dynamical Systems Approach (Graduate Studies in Mathematics) - Hardcover

Guido Schneider; Hannes Uecker

Hardcover

ISBN 10: 1470436132 ISBN 13: 9781470436131

Publisher: American Mathematical Society, 2017

Synopsis

This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs.The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrodinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given.The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.

About this title

About the Author

Guido Schneider, Universitat Stuttgart, Germany.Hannes Uecker, Carl von Ossietzky Universitat Oldenburg, Germany.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2017
• Language: English
• ISBN 10: 1470436132
• ISBN 13: 9781470436131
• Binding: Hardcover
• Number of pages: 575