Optimal control of the propagation of a graph in inhomogeneous media

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Deckelnick, Klaus ; Elliott, Charles M. ; Styles, Vanessa (2009)
  • Publisher: Society for Industrial and Applied Mathematics
  • Related identifiers: doi: 10.1137/080723648
  • Subject: QA
    acm: MathematicsofComputing_NUMERICALANALYSIS

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.
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