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Simple Singularities for Hamilton-Jacobi Equations with Max-Concave Hamiltonians and Generalized Characteristics

Author

Listed:
  • M. V. Day

    (Virginia Tech)

  • A. A. Melikyan

    (Institute for Problems in Mechanics)

Abstract

We consider piecewise smooth viscosity solutions to a Hamilton-Jacobi equation, for which the Hamiltonian is the maximum of a finite number of smooth concave functions. We describe the possible types of “basic” singularities, namely jump discontinuities in either the derivative of the solution or the Hamiltonian, which occur across a smooth hypersurface. Each such type of singularity is described in terms of the properties of the Hamiltonian and the classical characteristics in the regions on either side of the singularity. Where appropriate, singular characteristic equations of the types developed by Melikyan are formulated which can be used in constructions.

Suggested Citation

  • M. V. Day & A. A. Melikyan, 2008. "Simple Singularities for Hamilton-Jacobi Equations with Max-Concave Hamiltonians and Generalized Characteristics," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 155-174, August.
    • Handle: RePEc:spr:joptap:v:138:y:2008:i:2:d:10.1007_s10957-008-9372-8
    DOI: 10.1007/s10957-008-9372-8
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    References listed on IDEAS

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    1. Rami Atar & Paul Dupuis & Adam Shwartz, 2003. "An Escape-Time Criterion for Queueing Networks: Asymptotic Risk-Sensitive Control via Differential Games," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 801-835, November.
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