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Vladikavkazskii Matematicheskii Zhurnal, 2012, Volume 14, Number 4, Pages 19–23 (Mi vmj443)  
Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case

V. V. Gusachenkoa, V. B. Levenshtambc

a Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences, Russia, Rostov-on-Don
b South Mathematical Institute of VSC RAS, Russia, Vladikavkaz
c Southern Federal University, Chair of Algebras and Discrete Mathematics, Russia, Rostov-on-Don
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Abstract: A concrete (illustrative) example of the linear parabolic problem with two independent variables and high-frequency coefficients in time is considered. The corresponding stationary homogeneous averaged problem is degenerate. Using the method developed recently for an ordinary differential equations [1] and the method of boundary layer a full formal asymptotics of the periodic solution in time is constructed.
Key words: parabolic problem, high-frequency coefficient, averaged problem, full asymptotics.
Received: 20.11.2012
Document Type: Article
UDC: 517.633
Language: Russian
Citation: V. V. Gusachenko, V. B. Levenshtam, “Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case”, Vladikavkaz. Mat. Zh., 14:4 (2012), 19–23
Citation in format AMSBIB
\Bibitem{GusLev12}
\by V.~V.~Gusachenko, V.~B.~Levenshtam
\paper Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case
\jour Vladikavkaz. Mat. Zh.
\yr 2012
\vol 14
\issue 4
\pages 19--23
\mathnet{http://mi.mathnet.ru/vmj443}
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