Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 19-23
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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.
@article{VMJ_2012_14_4_a2,
author = {V. V. Gusachenko and V. B. Levenshtam},
title = {Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {19--23},
publisher = {mathdoc},
volume = {14},
number = {4},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a2/}
}
TY - JOUR AU - V. V. Gusachenko AU - V. B. Levenshtam TI - Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case JO - Vladikavkazskij matematičeskij žurnal PY - 2012 SP - 19 EP - 23 VL - 14 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a2/ LA - ru ID - VMJ_2012_14_4_a2 ER -
%0 Journal Article %A V. V. Gusachenko %A V. B. Levenshtam %T Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case %J Vladikavkazskij matematičeskij žurnal %D 2012 %P 19-23 %V 14 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a2/ %G ru %F VMJ_2012_14_4_a2
V. V. Gusachenko; V. B. Levenshtam. Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 19-23. http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a2/