Well-posedness of parabolic equations containing hysteresis with diffusive thresholds

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.

Авторы
Gurevich P. 1, 2 , Rachinskii D.3, 4
Номер выпуска
1
Язык
Английский
Страницы
87-109
Статус
Опубликовано
Том
283
Год
2013
Организации
  • 1 Free Univ Berlin, D-14195 Berlin, Germany
  • 2 Peoples Friendship Univ Russia, Moscow 117198, Russia
  • 3 Univ Texas Dallas, Dept Math Sci, Richardson, TX 75080 USA
  • 4 Natl Univ Ireland Univ Coll Cork, Dept Appl Math, Cork, Ireland
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/8457/