Dynamics of Partial Differential Equations

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book Dynamics of Partial Differential Equations by C. Eugene Wayne, Michael I. Weinstein, Springer International Publishing
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Author: C. Eugene Wayne, Michael I. Weinstein ISBN: 9783319199351
Publisher: Springer International Publishing Publication: August 8, 2015
Imprint: Springer Language: English
Author: C. Eugene Wayne, Michael I. Weinstein
ISBN: 9783319199351
Publisher: Springer International Publishing
Publication: August 8, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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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