Abstract
The nonstationary Poiseuille solution describing the flow of a viscous incompressible fluid in an infinite cylinder is defined as a solution of the inverse problem for the heat equation. The existence and uniqueness of such nonstationary Poiseuille solution with the prescribed flux F(t) of the velocity field is studied. It is proved that under some compatibility conditions on the initial data and flux F(t) the corresponding inverse problem has a unique solution in Holder spaces.
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