On the Behavior of a Nonstationary Poiseuille Solution as <Emphasis Type="Italic">t</Emphasis> → ∞

A nonstationary Poiseuille solution describing the flow of a viscous incompressible fluid in an infinite cylinder is defined as a solution to an inverse problem for the heat equation. The behavior as t → ∞ of the nonstationary Poiseuille solution corresponding to the prescribed flux F(t) ofthe velocity field is studied. In particular, it is proved that if the flux F(t) tends exponentially to a constant flux F _* then the nonstationary Poiseuille solution tends exponentially as t → ∞ to the stationary Poiseuille solution having the flux F _*.Original Russian Text Copyright © 2005 Pileckas K.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 890–900, July–August, 2005.