Finite-difference scheme for two-scale homogenized equations of one-dimensional motion of a thermoviscoelastic Voigt-type body

A. A. Amosov, A. E. Vestfal'skii

Department of Mathematical Modeling, Moscow Power Engineering Institute (Technical University), ul. Krasnokazarmennaya 14, Moscow, 111250, Russia

Abstract: The Bakhvalov–Eglit two-scale homogenized equations are used to describe the motion of layered periodic compressible media with rapidly oscillating data. A new finite-difference scheme for a system of such equations is proposed and analyzed in the case of a thermoviscoelastic Voigt-type body. A priori estimates of solutions are derived for nonsmooth data. The existence and uniqueness of discrete solutions are established. A theorem is proved on the convergence of a subsequence of discrete solutions to a weak solution of the problem under study. Simultaneously, a new theorem on the existence of global weak solutions is deduced.

Key words: finite-difference scheme, two-scale homogenized equations, thermoviscoelastic Voigt-type body, global weak solution.

UDC: 519.934

Received: 11.11.2005

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:4, 691–718

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