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商品詳細
Dynamics of Partial Differential Equations. 1st ed. 2015.
・ISBN 978-3-319-19934-4 paper EUR 39.99
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| 著者・編者 | Wayne, C. Eugene / Weinstein, Michael I., |
|---|---|
| シリーズ | Frontiers in Applied Dynamical Systems: Reviews and Tutorials |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2015 |
| ページ数 | 79 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-18937＞ |
解説
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently.
Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation.
The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.