Optimal Propagating Fronts Using Hamilton-Jacobi Equations

Autor:	Angelo Alessandri, Patrizia Bagnerini, Roberto Cianci, Mauro Gaggero
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	hamilton-jacobi equation normal flow equation level set methods optimization Mathematics QA1-939
Zdroj:	Mathematics, Vol 7, Iss 11, p 1122 (2019)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math7111122
Popis:	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.
Databáze:	Directory of Open Access Journals
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