Averaging of evolution system with boundary conditions

Authors: V. B. Levenshtam, P. E. Shubin

Keywords: Boundary value problem; high frequency; method of averaging

Abstract:

Method of averaging was justified for normal differential equations with a large parameter and boundary conditions on a segment and on the half-axis. Illustrative examples are given in both cases.

References:

[1] Bogolyubov, N.N., Yu, Mitropolsky.A. (1974) Asymptotic methods in theory of non-linear oscillations. Moscow: St. Publish [2] Bogolyubov, N.N. (1945) On some statistical methods in mathematical physics. Kiev: Publishing AN UkrSSR [3] Godunov, S.K. (1994) Ordinary differential equations with constant coefficients. Novosibirsk: Publishing University of Novosibirsk [4] Kolmogorov, A.N., Fomin, S.V. (1981) Elements of functional theory and functional analysis. Moskva: Nauka, in Russian [5] Simonenko, I.B. (1970) A justification of the averaging method for abstract parabolic equations. Mathematics of the USSR-Sbornik, 10(1): 51-59


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