Saturday, August 12

MS52
Concentrations in Reaction-Diffusion Systems

4:00 pm-6:30 PM
Anthurium & Ginger (Saloon 1 & 2)

It is believed that diffusion does not result in formation and dynamics of patterns, since it is smoothing and trivializing process. In fact, this is the case for a single reaction-diffusion equation. However, in recent years, a surprising variety of spatio-temporal patterns have been observed in all areas of science, within reaction-diffusion systems. The speakers in this minisyposium will discuss formation as well as dynamics of concentrations (spikes, blow-ups) arising in reaction-diffusion systems, such as Gierer-Meinhardt system in biological pattern formation, and the Gray-Scott model. They hope to open new directions for research, leading to improved analytical tools for studying these problems.

4:00-4:25 Spots for Two-Dimensional Activator-Inhibitor Systems

Matthias Winter, University of Stuttgart, Germany

4:30-4:55 Dynamics of Lotka Volterra Competition Systems with Large Interactions

E.N. Dancer, University of Sydney, Australia

5:00-5:25 To be announced

Yasumasa Nishiura, Research Institute for Electronic Science, Japan

5:30-5:55 An Abstract Setting for the Existence and Stability of the Spike Layer Solutions

Peter W. Bates, Brigham Young University, USA; E. Norman Dancer, University of Sydney, Australia; and Junping Shi, Tulane University, USA

6:00-6:25 No Interior Peaks for the Singular Perturbation Problem with Critical Exponent

N. Ghoussoub, University of British Columbia, Canada