Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case

Gusachenko V. V. , Levenshtam, V. B.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 4.

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.

Keywords: parabolic problem, high-frequency coefficient, averaged problem, full asymptotics

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