The next meeting of the seminar on Differential Equations and Mathematical Physics will be held online on June 22, 2022, at 2 p.m. (UTC+3).

A talk on

On Contact Defects in Reaction-Diffusion Systems

will be delivered by Dr. Milen Ivanov.

Abstract: Solutions of reaction-diffusion systems exhibit a wide variety of patterns like spirals, stripes and Turing patterns. In particular, the Belousov-Zhabotinsky (BZ) reaction produces spiral patterns, which may undergo a period-doubling bifurcation; then a line defect is emitted from the center of the spiral and along it the pattern jumps half a period. In order to study this phenomenon, we consider the so-called contact defects, studied by Sandstede and Scheel: functions, which converge (in an appropriate sense) to a periodic function as x→±∞. Of interest is the problem of truncating such a defect to a large interval, with Neumann or periodic boundary conditions. 

We will discuss the existence, uniqueness and spectral stability of such a truncated contact defect. It will turn out contact defect is spectrally stable when given periodic boundary conditions, and spectrally unstable with Neumann boundary conditions. These results suggest that the observed spiral patterns with line defects are stable.

Join Zoom Meeting:

https://us02web.zoom.us/j/84907200931?pwd=dlBQSEZjb04zank0WGJxeWJsZHNidz09

Meeting ID: 849 0720 0931
Passcode: 483873

Everybody is invited.

Department of Differential Equations and Mathematical Physics