Optimal Propagating Fronts Using Hamilton-Jacobi Equations

Angelo Alessandri, Patrizia Bagnerini, Roberto Cianci and Mauro Gaggero
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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

Mathematics, 2019, vol. 7, issue 11, 1-10

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.

Keywords: Hamilton-Jacobi equation; normal flow equation; level set methods; optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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