Spectral and Dynamical Stability of Nonlinear Waves

This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes the fundamental ideas of the past two decades of research, carefully balancing theory and application.

This book fills an important gap in the literature, bridging PDE and dynamical systems approach to stability Presents a unified treatment of the dynamical systems and functional analysis background of nonlinear stability Includes illustrative examples and a variety of exercises

Autorentext

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.

Inhalt
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.