Abstract
A new approach to solving averaging problems for micro-inhomogeneous continua, based on a restatement of the problem in terms of distribution functions, is described. Problems having a variational structure are considered. It is shown that, in terms of distribution functions, they reduce to the problem of minimizing a linear functional, having the meaning of the expectation value of the energy, in a set of distribution functions which is distinguished by an infinite number of linear constants. These constraints express certain matching conditions and contain multipoint distribution functions of the random characteristics of the medium. The constraints form an unlinked chain, the break of which at the n-th step contains only n-point distribution functions. In view of this, a sequence of approximate problems arises.
Published Version
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