Systems of reaction-Diffusion equations with spatially distributed hysteresis

We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vectorvalued function of space and time. Such systems describe hysteretic interaction of nondiffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity of hysteresis. These conditions are formulated in terms of geometry of the manifolds defining the hysteresis thresholds and the spatial profile of the initial data. © 2014, (publisher). All rights reserved.

Авторы
Gurevich P. 1, 2 , Tikhomirov S.3, 4
Журнал
Издательство
Akademie ved Ceske Republiky
Номер выпуска
2
Язык
Английский
Страницы
239-257
Статус
Опубликовано
Номер
A010
Том
139
Год
2014
Организации
  • 1 Pavel Gurevich, Free University Berlin, Arnimallee 3, Berlin, 14195, Germany
  • 2 Peoples’ Friendship University, Mikluho-Maklaya str. 6, Moscow, 117198, Russian Federation
  • 3 Sergey Tikhomirov, Chebyshev Laboratory, Saint-Petersburg State University, 14th line of Vasilievsky island, 29B, Saint-Petersburg, 199178, Russian Federation
  • 4 Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany
Ключевые слова
Reaction-diffusion equation; Spatially distributed hysteresis; Well-posedness
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5006/