Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Deckelnick, Klaus; Elliott, Charles M.; Styles, Vanessa (2009)
Publisher: Society for Industrial and Applied Mathematics
Languages: English
Types: Article
Subjects: QA

Classified by OpenAIRE into

ACM Ref: 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.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] G. Barles and P. E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, Asymptotic Anal., 4 (1991), pp. 271-283.
    • [2] J. M. Berg, A. Yezzi, and A. R. Tannenbaum, Phase transitions, curve evolution and the control of semiconductor manufacturing processes, in Proceedings of the IEEE Conference on Decision and Control, Kobe, Japan, 1996, pp. 3376-3381.
    • [3] J. M. Berg and N. Zhou, Shape-based optimal estimation and design of curve evolution processes with application to plasma etching, IEEE Trans. Automat. Control, 46 (2001), pp. 1862-1873.
    • [4] C. Castro, F. Palacios, and E. Zuazua, An alternating descent method for the optimal control of the inviscid Burgers equation in the presence of shocks, Math. Models Methods Appl. Sci., 18 (2008), pp. 369-416.
    • [5] M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277 (1983), pp. 1-42.
    • [6] M. G. Crandall, L. C. Evans, and P. L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 282 (1984), pp. 487-502.
    • [7] K. Deckelnick and C. M. Elliott, Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities, Interfaces Free Bound., 6 (2004), pp. 329-349.
    • [8] K. Deckelnick and C. M. Elliott, Propagation of graphs in two-dimensional inhomogeneous media, Appl. Numer. Math., 56 (2006), pp. 1163-1178.
    • [9] H. Ishii, Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets, Bull. Fac. Sci. Engrg. Chuo. Univ., 28 (1985), pp. 33-77.
    • [10] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr. 24, AMS, Providence, RI, 1968.
    • [11] S. Leung and J. Qian, An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals, Commun. Math. Sci., 4 (2006), pp. 249-266.
    • [12] J. A. Sethian, Level Set Methods, Cambridge University Press, Cambridge, UK, 1996.
    • [13] S. Ulbrich, A sensitivity and adjoint calculus for discontinuous solutions of hyperbolic conservation laws with source terms, SIAM J. Control Optim., 41 (2002), pp. 740-797.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article