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Optimal control of the propagation of a graph in inhomogeneous media

by Deckelnick, K., Elliott, C.M., Styles, V..

Series: 2008-08, Preprints

49J20 Optimal control problems involving partial differential equations
49L25 Viscosity solutions
49M25 Discrete approximations

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 a dual norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results.

Optimal control, eikonal equation, Hamilton-Jacobi equation, approximate controllability