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Optimal Propagating Fronts Using Hamilton-Jacobi Equations

Author

Listed:
  • Angelo Alessandri

    (Department of Mechanical Engineering (DIME), University of Genoa, 16145 Genoa, Italy)

  • Patrizia Bagnerini

    (Department of Mechanical Engineering (DIME), University of Genoa, 16145 Genoa, Italy)

  • Roberto Cianci

    (Department of Mechanical Engineering (DIME), University of Genoa, 16145 Genoa, Italy)

  • Mauro Gaggero

    (Institute of Marine Engineering (INM), National Research Council of Italy, Via De Marini 6, 16149 Genoa, Italy)

Abstract

The optimal handling of level sets associated to the solution of Hamilton-Jacobi equations such as the normal flow equation is investigated. The goal is to find the normal velocity minimizing a suitable cost functional that accounts for a desired behavior of level sets over time. Sufficient conditions of optimality are derived that require the solution of a system of nonlinear Hamilton-Jacobi equations. Since finding analytic solutions is difficult in general, the use of numerical methods to obtain approximate solutions is addressed by dealing with some case studies in two and three dimensions.

Suggested Citation

  • Angelo Alessandri & Patrizia Bagnerini & Roberto Cianci & Mauro Gaggero, 2019. "Optimal Propagating Fronts Using Hamilton-Jacobi Equations," Mathematics, MDPI, vol. 7(11), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1122-:d:287799
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    References listed on IDEAS

    as
    1. R. W. Beard & G. N. Saridis & J. T. Wen, 1998. "Approximate Solutions to the Time-Invariant Hamilton–Jacobi–Bellman Equation," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 589-626, March.
    2. R. Zoppoli & M. Sanguineti & T. Parisini, 2002. "Approximating Networks and Extended Ritz Method for the Solution of Functional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 403-440, February.
    3. Imane Abouelkheir & Fadwa El Kihal & Mostafa Rachik & Ilias Elmouki, 2019. "Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity," Mathematics, MDPI, vol. 7(5), pages 1-21, May.
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