AVERAGING ON A BACKGROUND OF VANISHING VISCOSITY
Serguei M. Kozlov, A L Pyatnitskiĭ · Mathematics of the USSR-Sbornik · 1991
Elliptic equations of the form with periodic coefficients are considered; and are small parameters. For potential fields and constants , the asymptotic behavior as of the coefficients of the averaged operator (which is customarily also called the effective diffusion) is studied. It is shown that as the effective diffusion decays exponentially, and the limit is found.Sufficient conditions are found for the existence of a limit operator as and tend to 0 simultaneously. The structure of this operator depends on the symmetry reserve of the coefficients and ; in particular, it may decompose into independent operators in subspaces of lower dimension.