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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1983 Volume 122(164), Number 2(10), Pages 220–231 (Mi sm2286)

This article is cited in 5 papers

Averaging processes in framework structures

G. P. Panasenko


Abstract: Equations of hyperbolic, parabolic, and elliptic types are considered on an $m$-dimensional framework – the union over all $j=1,\dots,m$ of systems, $\varepsilon$-periodic ($\varepsilon\ll1$) in all variables, of thin beams of strips (with transverse dimension $\varepsilon\mu$, $\mu\ll1$) oriented in the $j$th coordinate direction. Asymptotic expansions of solutions are constructed.
Figures: 3.
Bibliography: 22 titles.

UDC: 517.946.9

MSC: Primary 35G15, 35B40; Secondary 73K05

Received: 27.11.1981


 English version:
Mathematics of the USSR-Sbornik, 1985, 50:1, 213–225

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© Steklov Math. Inst. of RAS, 2024