Simple Singularities for Hamilton-Jacobi Equations with Max-Concave Hamiltonians and Generalized Characteristics |
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Authors: | M V Day A A Melikyan |
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Institution: | (1) Department of Mathematics, Virginia Tech, Blacksburg, VA, USA;(2) Institute for Problems in Mechanics, Moscow, Russia |
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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. |
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Keywords: | Differential games Viscosity solutions Singular surfaces Generalized characteristics |
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