  We study Hamilton-Jacobi equations in [0, +$\infty$) of evolution type with
nonlinear boundary conditions of Neumann type in the case where the Hamiltonian
is non necessarily convex with respect to the gradient variable. In this paper,
we give two main results. First, we prove a classification of boundary
condition result for a nonconvex, coercive Hamiltonian, in the spirit of the
flux-limited formulation for quasi-convex Hamilton-Jacobi equations on networks
recently introduced by Imbert and Monneau. Second, we give a comparison
principle for a nonconvex and noncoercive Hamiltonian where the boundary
condition can have flat parts.
