Backward energy-flux for spherically symmetric scalar waves

I consider spherically symmetric scalar waves of two types: explosive waves in an infinite medium generated by a spherically symmetric source, and implosive waves in which the medium is contained inside a spherically symmetric source. The explosive waves travel outward, the implosive waves inward. Although there are exceptional cases, in general there are, at any time, shells in which the energy-flux is opposed to the sense of propagation of the waves.