Nonlinear PDEs
A Dynamical Systems Approach
Seiten
2017
American Mathematical Society (Verlag)
978-1-4704-3613-1 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-3613-1 (ISBN)
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.
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.
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.
Guido Schneider, Universitat Stuttgart, Germany. Hannes Uecker, Carl von Ossietzky Universitat Oldenburg, Germany.
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.
| Erscheinungsdatum | 12.11.2017 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 1160 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-3613-2 / 1470436132 |
| ISBN-13 | 978-1-4704-3613-1 / 9781470436131 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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