Preprint series: 08-08, Preprints
- 49J20 Optimal control problems involving partial differential equations
- 49L25 Viscosity solutions
- 49M25 Finite difference methods
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
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