A construction procedure using characteristics for viscosity solutions of the Hamilton-Jacobi equation

This paper provides a procedure to generate C/sub 1/ or (C/sub 0/, PC/sub 1/) solutions of a 1D Hamilton-Jacobi equation with a non-smooth Hamiltonian, based on the method of characteristics. The C/sub 1/ solutions constructed are classical solutions. We prove, using examples, that the (C/sub 0/, PC/sub 1/) constructed solutions are the viscosity solutions, with help of a minimax-viscosity equivalence. We show how shock waves and voids are generated by initial conditions. We show with 2D examples how this technique might be applied to differential games.