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Журнал вычислительной математики и математической физики, 2018, том 58, номер 12, статья опубликована в англоязычной версии журнала
(Mi zvmmf10872)
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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Статьи, опубликованные в английской версии журнала
Existence, asymptotics, stability and region of attraction of a periodic boundary layer solution in case of a double root of the degenerate equation
V. F. Butuzova, N. N. Nefedova, L. Reckeb, K. R. Schneiderc a Faculty of Physics, Moscow State University, Moscow, Russia
b HU Berlin, Institut für Mathematik, Berlin-Adlershof, Germany
c Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Аннотация:
For a singularly perturbed parabolic problem with Dirichlet conditions we prove the existence of a solution periodic in time and with boundary layers at both ends of the space interval in the case that the degenerate equation has a double root. We construct the corresponding asymptotic expansion in the small parameter. It turns out that the algorithm of the construction of the boundary layer functions and the behavior of the solution in the boundary layers essentially differ from that ones in case of a simple root. We also investigate the stability of this solution and the corresponding region of attraction.
Ключевые слова:
singularly perturbed reaction-diffusion equation, double root of the degenerate equation, initial boundary value problem, asymptotic expansion, asymptotically stable periodic solution, region of attraction.
Поступила в редакцию: 03.03.2017
Образец цитирования:
V. F. Butuzov, N. N. Nefedov, L. Recke, K. R. Schneider, “Existence, asymptotics, stability and region of attraction of a periodic boundary layer solution in case of a double root of the degenerate equation”, Comput. Math. Math. Phys., 58:12 (2018), 1989–2001
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/zvmmf10872
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