A9: Reaction-diffusion systems: hysteresis and nonlocal interactions

Principal investigator:

PD Dr. Pavel Gurevich [1]

Summary:

The project deals with reaction-diffusion systems involving hysteresis, or, more generally, bistability. The
models under consideration have applications to a large number of biological, chemical, physical, and
economic processes. Besides the nontrivial issue of well-posedness, we are interested in the qualitative
description of solutions. The analysis will be in terms of emerging spatio-temporal patterns that are
influenced primarily by the interplay between diffusion and spatially distributed hysteresis. We will also
develop theoretical concepts for the stability analysis and control of these patterns by temporally and
spatially nonlocal feedback.