  We present a study of the Adomian's Decomposition Method (ADM) applied to the
Hamilton-Jacobi equations ut + H (ux) = 0. We recall the well known
characteristics methods in the case of this type of equations to justify the
existence or not of solutions. This yields that the ADM gives efficient
solutions in time only in ]0; T *[, where T * is the critical time of our
equation.
