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On the Unsteady Potential Plane Flow Past a Porous Circle

We consider a nonstationary plane flow which is an ideal flow on the whole plane except on a circle. On the circle we assume inhomogeneous in time and position linear dependence between normal velocity and pressure difference. We reduce the problem to an operator differential equation with an initial condition and by use of partial differential equation theory from Lions and Magenes we prove the existence and uniqueness of a solution for t ϵ [0, ∞). For periodic in time input conditions we prove the existence and uniqueness of a periodic solution of the problem. We also consider the solution by time independent input conditions. In this case the solution has a limit in infinity and tends exponentially to this limit.