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Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow

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  • A time-dependent Stokes fluid flow problem is studied with nonlinear boundary conditions described by the Clarke subdifferential. We present equivalent weak formulations of the problem, one of them in the form of a hemivariational inequality. The existence of a solution is shown through a limiting procedure based on temporally semi-discrete approximations. Uniqueness of the solution and its continuous dependence on data are also established. Finally, we present a result on the existence of a solution to an optimal control problem for the hemivariational inequality.
    Mathematics Subject Classification: Primary: 35A15, 35A35; Secondary: 49J20.

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