Asymptotic integration of linear system with high-frequency coefficients and Stokes operator in the main part

Article type: Research Article

Authors: Levenshtam, V.B.^; | Ishmeev, M.R.

Affiliations: Department of Mathematics, Mechanics and Computer Science, South Federal University, Milchakova Street 8a, Rostov-on-Don, Russia

Note: [] Corresponding author. E-mail: [email protected]

Abstract: A linear system of integro-differential equations with Stokes operator in the main part and with rapidly oscillating by time terms is considered. The corresponding stationary limiting (averaged) problem has zero eigenvalue, and corresponding eigenfunction has generalized associated first order function in the Vishik–Lyusternik sense. A complete asymptotic expansion of time-periodic solution is constructed and proved.

Keywords: system of integro-differential equations, Stokes operator, complete asymptotic expansion, rapidly oscillating items, averaging method

DOI: 10.3233/ASY-151284

Journal: Asymptotic Analysis, vol. 92, no. 3-4, pp. 363-376, 2015