Periodic Solutions with a Boundary Layerof Reaction–Diffusion Equations with SingularlyPerturbed Neumann Boundary Conditions

Авторы: Butuzov V.F., Nefedov N.N., Recke L., Schneider K.R.
Журнал: International Journal of Bifurcation and Chaos,
Том: 24
Номер: 8
Год издания: 2014
Первая страница: 1440019-1
Последняя страница: 1440019-8
DOI: 10.1142/S0218127414400197
Аннотация: We consider singularly perturbed reaction–diffusion equations with singularly perturbed Neumann boundary conditions. We establish the existence of a time-periodic solution u(x, t, ε) with boundary layers and derive conditions for their asymptotic stability. The boundary layer part of u(x, t, ε) is of order one, which distinguishes our case from the case of regularly perturbed Neumann boundary conditions, where the boundary layer is of order ε. Another peculiarity of our problem is that — in contrast to the case of Dirichlet boundary conditions — it may have several asymptotically stable time-periodic solutions, where these solutions differ only in the description of the boundary layers. Our approach is based on the construction of sufficiently precise lower and upper solutions.
Добавил в систему: Нефедов Николай Николаевич

	ИСТИНА	Войти в систему Регистрация
	ИСТИНА ЦЭМИ РАН
	Главная Поиск Статистика О проекте Помощь

ИСТИНА