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Dynamics of partial differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamics of partial differential equationsby C. Eugene Wayne, Michael I. Weinstein.
Author:	Wayne, C. Eugene.
other author:	Weinstein, Michael I.
Published:	Cham :Springer International Publishing :2015.
Description:	x, 79 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential equations, Partial.
Online resource:	http://dx.doi.org/10.1007/978-3-319-19935-1
ISBN:	9783319199351$q(electronic bk.)

Dynamics of partial differential equations
Wayne, C. Eugene.

Dynamics of partial differential equations[electronic resource] /by C. Eugene Wayne, Michael I. Weinstein. - Cham :Springer International Publishing :2015. - x, 79 p. :ill., digital ;24 cm. - Frontiers in applied dynamical systems: reviews and tutorials,v.32364-4532 ;. - Frontiers in applied dynamical systems: reviews and tutorials ;v.3..

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.

ISBN: 9783319199351$q(electronic bk.)

Standard No.: 10.1007/978-3-319-19935-1doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Dynamics of partial differential equations
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245 1 0 $a Dynamics of partial differential equations $h [electronic resource] / $c by C. Eugene Wayne, Michael I. Weinstein.
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300 $a x, 79 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in applied dynamical systems: reviews and tutorials, $x 2364-4532 ; $v v.3
520 $a 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.
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