  We study well posedness of time--dependent Hamilton--Jacobi equations on a
network, coupled with a continuous initial datum and a flux limiter. We show
existence and uniqueness of solutions as well as stability properties. The
novelty of our approach is that comparison results are proved linking the
equation to a suitable semidiscrete problem, bypassing doubling variable
method. Further, we do not need special test functions, and perform tests
relative to the equations on different arcs separately.
