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Optimal control of the propagation of a graph in inhomogeneous media
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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. 13351352. ISSN 03630129

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Official URL: http://dx.doi.org/10.1137/080723648
Abstract
We study an optimal control problem for viscosity solutions of a Hamilton–Jacobi equation describing the propagation of a onedimensional 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 > Mathematics 
Library of Congress Subject Headings (LCSH):  Differential equations, Partial  Research, Eikonal equation, HamiltonJacobi equations, Approximation theory 
Journal or Publication Title:  SIAM Journal on Control and Optimization 
Publisher:  Society for Industrial and Applied Mathematics 
ISSN:  03630129 
Official Date:  15 April 2009 
Volume:  Vol.48 
Number:  No.3 
Page Range:  pp. 13351352 
Identification Number:  10.1137/080723648 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  # G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, Asymptotic Anal., 4 (1991), pp. 271–283. 
URI:  http://wrap.warwick.ac.uk/id/eprint/2210 
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