naa a22 4500 510811272 CHVBK 20180411083443.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1134/S0081543813080075 doi (NATIONALLICENCE)springer-10.1134/S0081543813080075 Well-posedness of parabolic equations containing hysteresis with diffusive thresholds [Elektronische Daten] [Pavel Gurevich, Dmitrii Rachinskii] We study complex systems arising, in particular, in population dynamics, developmental biology, and bacterial metabolic processes, in which each individual element obeys a relatively simple hysteresis law (a non-ideal relay). Assuming that hysteresis thresholds fluctuate, we consider the arising reaction-diffusion system. In this case, the spatial variable corresponds to the hysteresis threshold. We describe the collective behavior of such a system in terms of the Preisach operator with time-dependent measure which is a part of the solution for the whole system. We prove the well-posedness of the system and discuss the long-term behavior of solutions. Pleiades Publishing, Ltd., 2013 Gurevich Pavel Freie Universität Berlin, Kaiserswerther Str. 16-18, 14195, Berlin, Germany aut Rachinskii Dmitrii Department of Mathematical Sciences, University of Texas at Dallas, FO 35, 800 West Campbell Road, 75080-3021, Richardson, TX, USA aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 283/1(2013-12-01), 87-109 0081-5438 283:1<87 2013 283 11501 https://doi.org/10.1134/S0081543813080075 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813080075 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gurevich Pavel Freie Universität Berlin, Kaiserswerther Str. 16-18, 14195, Berlin, Germany aut NATIONALLICENCE 700 1- Rachinskii Dmitrii Department of Mathematical Sciences, University of Texas at Dallas, FO 35, 800 West Campbell Road, 75080-3021, Richardson, TX, USA aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 283/1(2013-12-01), 87-109 0081-5438 283:1<87 2013 283 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer