Nonlinear PDEs : a dynamical systems approach

Author(s)

• Schneider, Guido
• Uecker, Hannes

Bibliographic Information

Nonlinear PDEs : a dynamical systems approach

Guido Schneider, Hannes Uecker

（Graduate studies in mathematics, v. 182）

American Mathematical Society, c2017

Note

"Applied mathematics"--Cover

Includes bibliographical references (p. 541-566) and index

Description and Table of Contents

Description

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.

Table of Contents

Basic ODE dynamics Dissipative dynamics Hamiltonian dynamics PDEs on an interval The Navier-Stokes equations Some dissipative PDE models Three canonical modular equations Reaction-diffusion systems Dynamics of pattern and the GL equation Wave packets and the NLS equation Long waves and their modular equations Center manifold reduction and spatial dynamics Diffusive stability Bibliography Index List of symbols.

by "Nielsen BookData"

Details

• NCID: BB24830513
• ISBN:
  • 9781470436131
• LCCN: 2017012328
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: xiii, 575 p.
• Size: 27 cm
• Classification:
  • LCC : QA377
  • DC23 : 515/.353
• Subject Headings:
  • LCSH : Differential equations, Partial
  • LCSH : Differential equations, Nonlinear
• Parent Bibliography ID:
  • BA20542214