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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. 1335-1352. ISSN 0363-0129

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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 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 > 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

Identification Number:

10.1137/080723648

Status:

Peer Reviewed

Access rights to Published version:

Open Access

References:

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URI:

http://wrap.warwick.ac.uk/id/eprint/2210

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