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Dynamics of partial differential equations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Dynamics of partial differential equations/ by 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

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

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

527784
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Dynamics of partial differential equations
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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.
650 0 $a Differential equations, Partial. $3 527784
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
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830 0 $a Frontiers in applied dynamical systems: reviews and tutorials ; $v v.3. $3 1067989
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950 $a Mathematics and Statistics (Springer-11649)