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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 6, Pages 988–1006
(Mi zvmmf4596)
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This article is cited in 1 scientific paper (total in 1 paper)
Substantiation of two-scale homogenization of the equations governing the longitudinal vibrations of a viscoelastoplastic Ishlinskii material
A. A. Amosov, I. A. Goshev Department of Mathematical Modeling, Moscow Power Engineering Institute (Technical University), ul. Krasnokazarmennaya 14, Moscow, 111250, Russia
Abstract:
Initial-boundary value problems for the system of quasilinear operator-differential equations governing the longitudinal vibrations of a viscoelastoplastic Ishlinskii material with nonsmooth rapidly oscillating coefficients and initial data are investigated. The system involves the hysteresis Prandtl–Ishlinskii operator. Passage to the limit to initial-boundary value problems for the corresponding system of two-scale homogenized operator integro-differential equations is strictly substantiated globally in time without assuming that the data are small.
Key words:
system of equations of longitudinal vibrations, viscoelastoplastic materials, method of two-scale homogenization, system of quasilinear operator-differential equations, initial-boundary value problem.
Received: 19.06.2006 Revised: 12.12.2006
Citation:
A. A. Amosov, I. A. Goshev, “Substantiation of two-scale homogenization of the equations governing the longitudinal vibrations of a viscoelastoplastic Ishlinskii material”, Zh. Vychisl. Mat. Mat. Fiz., 47:6 (2007), 988–1006; Comput. Math. Math. Phys., 47:6 (2007), 943–961
Linking options:
https://www.mathnet.ru/eng/zvmmf4596 https://www.mathnet.ru/eng/zvmmf/v47/i6/p988
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