Recent advances in reaction-diffusion equations with non-ideal relays

We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and solutions. We assert that the equation with transverse initial data possesses a unique solution, which remains transverse for some time, and also describe its regularity. At a moment when the solution becomes nontransverse, we discretize the spatial variable and analyze the resulting lattice dynamical system with hysteresis. In particular, we discuss a new pattern formation mechanism—rattling, which indicates how one should reset the continuous model to make it well posed. © Springer International Publishing Switzerland 2016.

Авторы
Curran M.1 , Gurevich P. 2, 3 , Tikhomirov S.4, 5
Редакторы
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Сборник статей
Издательство
Springer Verlag
Номер выпуска
-
Язык
Английский
Страницы
211-234
Статус
Опубликовано
Подразделение
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Ссылка
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Номер
-
Том
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Год
2016
Организации
  • 1 Institute of Mathematics I, Free University of Berlin, Arnimallee 7, Berlin, 14195, Germany
  • 2 Institute of Mathematics I, Free University of Berlin, Arnimallee 3, Berlin, 14195, Germany
  • 3 Peoples’ Friendship University of Russia, Miklukho-Maklaya Str. 6, Moscow, 117198, Russian Federation
  • 4 Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, Leipzig, 04103, Germany
  • 5 Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178, Russian Federation
Ключевые слова
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Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/4329/