Deckelnick, Klaus, Elliott, Charles M. and Styles, Vanessa (2009) Optimal control of the propagation of a graph in inhomogeneous media. SIAM Journal on Control and Optimization, Vol.48 (No.3). pp. 1335-1352. doi:10.1137/080723648 ISSN 0363-0129.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Differential equations, Partial -- Research, Eikonal equation, Hamilton-Jacobi equations, Approximation theory
Journal or Publication Title:	SIAM Journal on Control and Optimization
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0363-0129
Official Date:	15 April 2009
Dates:	Date Event 15 April 2009 Published
Volume:	Vol.48
Number:	No.3
Page Range:	pp. 1335-1352
DOI:	10.1137/080723648
Status:	Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)

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