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

M. V. Day () and A. A. Melikyan ()
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M. V. Day: Virginia Tech
A. A. Melikyan: Institute for Problems in Mechanics

Journal of Optimization Theory and Applications, 2008, vol. 138, issue 2, No 1, 155-174

Abstract: 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.

Keywords: Differential games; Viscosity solutions; Singular surfaces; Generalized characteristics (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-008-9372-8

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