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Optimal control of the propagation of a graph in inhomogeneous media

By Klaus Deckelnick, Charles M. Elliott and Vanessa Styles

Abstract

We study an optimal control problem for viscosity solutions of a Hamilton–Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the $H^{-1}$-norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results

Topics: QA
Publisher: Society for Industrial and Applied Mathematics
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:2210

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