Reaction-diffusion systems: hysteresis and nonlocal interactions (A09*)

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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.