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In this work, we study a boundary control problem for the evolutionary Stokes equations, under mixed boundary conditions, in two and three dimensions. The Stokes equation is a valuable tool in cardiovascular biomechanics, especially for modeling blood flow in low-velocity and high-viscosity conditions. Its application in the microvasculature, the design of medical devices, and the study of cardiovascular diseases helps improve the understanding and treatment of various pathological conditions. We provide a comprehensive theoretical framework to address the analysis and the derivation of a system of first-order optimality conditions that characterizes the solution of the control problem. Finally, solution-finding algorithm is proposed and illustrated with some simulations.
Irene Marín-Gayte (Mon,) studied this question.