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

**Series:** 2008-08, Preprints

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

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

**Keywords:**

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