This article is cited in 4 scientific papers (total in 4 papers)
Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation
Abstract:
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 a 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.
Keywords:singularly perturbed reaction-diffusion equation; asymptotic approximation; periodic solution; boundary layers; Lyapunov stability; region of attraction.
Citation:
V. F. Butuzov, N. N. Nefedov, L. Recke, K. Schneider, “Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation”, Model. Anal. Inform. Sist., 23:3 (2016), 248–258; Automatic Control and Computer Sciences, 51:7 (2017), 606–613
\Bibitem{ButNefRec16}
\by V.~F.~Butuzov, N.~N.~Nefedov, L.~Recke, K.~Schneider
\paper Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation
\jour Model. Anal. Inform. Sist.
\yr 2016
\vol 23
\issue 3
\pages 248--258
\mathnet{http://mi.mathnet.ru/mais495}
\crossref{https://doi.org/10.18255/1818-1015-2016-3-248-258}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3520847}
\elib{https://elibrary.ru/item.asp?id=26246291}
\transl
\jour Automatic Control and Computer Sciences
\yr 2017
\vol 51
\issue 7
\pages 606--613
\crossref{https://doi.org/10.3103%2FS0146411617070045}
Linking options:
https://www.mathnet.ru/eng/mais495
https://www.mathnet.ru/eng/mais/v23/i3/p248
This publication is cited in the following 4 articles: