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
https://doi.org/10.18255/1818-1015-2016-3-248-258
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.
About the Authors
V. F. Butuzov
Lomonosov Moscow State University
Russian Federation
119991, Moscow, Leninskie Gory, MSU, faculty of physics, Professor
Russian Federation
119991, Moscow, Leninskie Gory, MSU, faculty of physics, Professor
N. N. Nefedov
Lomonosov Moscow State University
Russian Federation
119991, Moscow, Leninskie Gory, MSU, faculty of physics, Professor
Russian Federation
119991, Moscow, Leninskie Gory, MSU, faculty of physics, Professor
L. Recke
HU Berlin, Institut fuЁr Mathematik, Rudower Chaussee, Berlin, Germany
Germany
Professor
Germany
Professor
K. Schneider
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, German
Germany
Professor
Germany
Professor
References
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Review
For citations:
Butuzov V.F., Nefedov N.N., Recke L., Schneider K. 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. Modeling and Analysis of Information Systems. 2016;23(3):248-258. (In Russ.) https://doi.org/10.18255/1818-1015-2016-3-248-258
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