Substantiation of two-scale homogenization of the equations governing the longitudinal vibrations of a viscoelastoplastic Ishlinskii material

A. A. Amosov   ; I. A. Goshev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 988-1006

Résumé

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.

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