Spectral and Dynamical Stability of Nonlinear Waves

Author:   Todd Kapitula ,  Keith Promislow
Publisher:   Springer-Verlag New York Inc.
Edition:   2013 ed.
Volume:   185
ISBN:  

9781493901876


Pages:   361
Publication Date:   08 July 2015
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Spectral and Dynamical Stability of Nonlinear Waves


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Author:   Todd Kapitula ,  Keith Promislow
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2013 ed.
Volume:   185
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   5.679kg
ISBN:  

9781493901876


ISBN 10:   1493901877
Pages:   361
Publication Date:   08 July 2015
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Introduction.- Background material and notation.- Essential and absolute spectra.- Dynamical implications of spectra: dissipative systems.- Dynamical implications of spectra: Hamiltonian systems.- Dynamical implications of spectra: Hamiltonian systems.- Point spectrum: reduction to finite-rank eigenvalue problems.- Point spectrum: linear Hamiltonian systems.- The Evans function for boundary value problems.- The Evans function for Sturm-Liouville operators on the real line.- The Evans function for nth-order operators on the real line.- Index.- References.    

Reviews

From the book reviews: This 368-page book provides an excellent introduction to the spectral and nonlinear stability theory of nonlinear waves in one-dimensional domains. It is aimed primarily at graduate students, but it can certainly also be used by postdocs and other researchers who are interested in learning more about this area. ... this book covers a broad range of topics in an area for which not many alternatives exist: the book is, in my opinion, an excellent addition to the literature. (Bjorn Sandstede, Dynamical Systems Magazine, dynamicalsystems.org, April, 2014) The book under review focuses on stability of the equilibria of evolution equations. ... The book consists of two parts. ... Each chapter contains exercises, bibliographic comments and additional reading information. The reviewer evaluates the book as a significant achievement and recommends it to all interested readers. (Radu Precup, zbMATH, Vol. 1297, 2014) This book by Kapitula and Promislow provides a quite unique entry point into this area, suitable for graduate students and young researchers who are interested in entering the field. ... An extensive bibliography and plenty of remarks at chapter endings then serve as a guide to history and current literature. This field has needed such a book as an entry point for graduate students, and the authors deserve a huge thanks from the community for putting it together. (Arnd Scheel, SIAM Review, Vol. 56 (3), 2014)


Author Information

Todd Kapitula is a Professor of Mathematics at Calvin College.  He previously held appointments at the University of New Mexico, Virginia Tech, the University of Utah, and Brown University.  He is the co-author of the 2008 Outstanding Paper Prize “Three is a crowd: solitary waves in photorefractive media with three potential wells”, SIAM J. Dyn. Sys. 5(4):598-633 (2006).  He is the author or co-author of over 40 research articles, and has been awarded several research grants from the National Science Foundation.   Keith Promislow is Professor of Mathematics at Michigan State University. His research interests include network morphology of amphiphilic systems induced  by charged-polymer solvent interactions. He serves on the editorial board of Physica D, SIAM Math Analysis, and SIAM Dynamical Systems. He represented the American Math Society at the Coalition for National Science Funding's 2011 Capital Hill Exhibit and was the 2010 Kloosterman Professor at the University of Leiden.  

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