Wednesday, May 26

The Continuous Spectrum and Its Implications for Pattern Formation

10:00 AM-12:00 PM
Room: Maybird

This minisymposium focuses on the role of the continuous spectrum for pattern formation in nonlinear partial differential equations on unbounded domains. The effects of the continuous spectrum are relevant to dynamical behavior near shocks, spiral waves and various travelling waves. The continuous spectrum may cause bifurcations to other patterns in various ways. On one hand, discrete eigenvalues may pop out of the continuous spectrum and cross the imaginary axis, resulting in a bifurcation which can be described by a finite-dimensional dynamical system. On the other hand, the continuous spectrum itself may cross the imaginary axis, thus destabilizing the asymptotic states of the underlying wave. This phenomena can also lead to the creation of new stable spatio-temporal patterns. In contrast to the aforementioned mechanism, the dynamical system which describes this bifurcation is in general infinite-dimensional. The speakers will discuss recent progress in the analysis of these mechanisms and their consequences for the applications.

Organizer: Todd Kapitula
University of New Mexico, Albuquergue
Björn Sandstede
Ohio State University, Columbus

10:00-10:25 Front Dynamics in a Spatially Discrete System
Neil J. Balmforth, University of California, Santa Cruz
10:30-10:55 Evans Function Analysis in the Continuous Spectrum and Applications
Robert Gardner, University of Massachusetts, Amherst
11:00-11:25 Essential Instability of Pulses, and Bifurcation to Modulated Travelling Waves
Björn Sanstede, Organizer; and Arnd Scheel, Freie Universität, Berlin, Germany
11:30-11:55 NEWExistence and Stability of Dark Solitons
Todd Kapitula, Organizer; and Jonathan Rubin, Ohio State University

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LMH, 1/11/99, MMD, 3/25/99