DFG
Collaborative Research Center 910 on
Control of selforganizing nonlinear systems
Research Project
Reactiondiffusion systems: hysteresis and nonlocal interactions
 Principal Investigator
 PD Dr. Pavel Gurevich
 Members
Dr. Nikita Begun (PostDoc): My main research interests include Dynamical systems, Differential equations, Reactiondiffusion equations, Hyperbolic attractors and systems with dry friction.
Mark Curran (PhD Student): I am interested in the wellposedness of reactiondiffusion equations with a nonlinear term involving spatially distributed hysteresis. In particular, I am dealing with this problem where the spatial domain is a subset of R^n with n greater than one.
Adem Güngör (Masters studentStudent Assistant)
Eyal Ron(Former PhD Student):I am interested in delay differential equations and hysteresis operators. Research questions invole longterm behaviour, such as periodic solutions and patterns. Specifically, the question of controlling these phenomenon using delay terms (e.g. Pyragas control) or hysteresis operators is of great interest.
Konstantinos Zemas (Former masters studentStudent Assistant)
Project Summary
The project deals with reactiondiffusion 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 wellposedness, we are interested in the qualitative description of solutions. The analysis will be in terms of emerging spatiotemporal 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.
Preprints and Publications
 Gurevich P., Tikhomirov S.

Spatially discrete reactiondiffusion equations with discontinuous hysteresis.
Preprint
(pdf)
 Gurevich P.

Asymptotics of parabolic Green's functions on lattices.
Preprint
(pdf)
 Gurevich P., Rachinskii D.

Asymptotics of signchanging patterns in hysteretic systems with diffusive thresholds.
Submitted
(pdf)
 Gurevich P., Vaeth M.

Stability for semilinear parabolic problems in L_2, W_2^1, and interpolation spaces.
Submitted
(pdf)
 Friedman G., Gurevich P., McCarthy S., Rachinskii D.

Switching behaviour of twophenotype bacteria in varying environment.
J. Physics: Conference Series. Vol. 585 (2015), 012012.
(pdf)
 Zeitz M., Gurevich P., Stark H.

Feedback control of flow vorticity at low Reynolds numbers.
The European Physical Journal E (EPJE). Vol. 38:22 (2015).
(pdf)
 Gurevich P., Rachinskii D.

Pattern formation in parabolic equations containing hysteresis with diffusive thresholds.
J. Math. Anal. Applications. Vol. 424 (2015), 11031124.
(pdf)
 N. A. Begun and S. G. Kryzhevich

Onedimensional chaos in a system with dry friction: analytical approach
Meccanica. 2015.
(pdf)
