Version 1
: Received: 30 August 2024 / Approved: 9 September 2024 / Online: 9 September 2024 (07:10:45 CEST)
How to cite:
Marín-Gayte, I. Optimal Boundary Control Problem for the Stokes Equation in Cardiovascular Applications. Preprints2024, 2024090631. https://doi.org/10.20944/preprints202409.0631.v1
Marín-Gayte, I. Optimal Boundary Control Problem for the Stokes Equation in Cardiovascular Applications. Preprints 2024, 2024090631. https://doi.org/10.20944/preprints202409.0631.v1
Marín-Gayte, I. Optimal Boundary Control Problem for the Stokes Equation in Cardiovascular Applications. Preprints2024, 2024090631. https://doi.org/10.20944/preprints202409.0631.v1
APA Style
Marín-Gayte, I. (2024). Optimal Boundary Control Problem for the Stokes Equation in Cardiovascular Applications. Preprints. https://doi.org/10.20944/preprints202409.0631.v1
Chicago/Turabian Style
Marín-Gayte, I. 2024 "Optimal Boundary Control Problem for the Stokes Equation in Cardiovascular Applications" Preprints. https://doi.org/10.20944/preprints202409.0631.v1
Abstract
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.
Keywords
optimal control; partial differential equations; fluid dynamics; stokes equation; total stress; boundary control; finite element method
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
