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Poro-Visco-Elasticity in Biomechanics: Optimal Control

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Research in Mathematics of Materials Science

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 31))

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Abstract

In this paper, we address optimal control problems subject to fluid flows through poro-visco-elastic media. In particular, we focus on the case of given permeability k(x, t), which translates into a convex control problem, with both distributed and boundary controls. We focus on investigating the problem of maintaining the solid displacement and Darcy pressure close to desired values (motivated by applications related to tissue perfusion in the eye and its relationship to the development of glaucoma) using the sources present in the system as control variables. The results provided in this paper include existence and uniqueness of optimal control, as well as the characterization of the optimal control through the first order necessary optimality conditions, based on the adjoint system.

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Acknowledgements

The authors were partially supported by L. Bociu’s NSF-DMS 1555062.

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Authors and Affiliations

  1. North Carolina State University, Department of Mathematics, Raleigh, NC, USA

    Lorena Bociu & Sarah Strikwerda

Authors
  1. Lorena Bociu
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  2. Sarah Strikwerda
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Correspondence to Lorena Bociu .

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Editors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA

    Malena I. Español

  2. Mathematics Department, University of Pittsburgh, Pittsburgh, PA, USA

    Marta Lewicka

  3. Department of Mathematics, Heriot-Watt University, Edinburgh, UK

    Lucia Scardia

  4. Institute of Mathematics, Universität Würzburg, Würzburg, Germany

    Anja Schlömerkemper

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Bociu, L., Strikwerda, S. (2022). Poro-Visco-Elasticity in Biomechanics: Optimal Control. In: Español, M.I., Lewicka, M., Scardia, L., Schlömerkemper, A. (eds) Research in Mathematics of Materials Science. Association for Women in Mathematics Series, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-031-04496-0_5

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