OPTIMAL CONTROL OF THE PROPAGATION OF A GRAPH IN INHOMOGENEOUS MEDIA.

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. [ABSTRACT FROM AUTHOR]