  The time evolution of self-interacting spherically symmetric scalar fields in
Minkowski spacetime is investigated based on the use of Green's theorem. It is
shown that a massive Klein-Gordon field can be characterized by the formation
of certain expanding shell structures where all the shells are built up by very
high frequency oscillations. This oscillation is found to be modulated by the
product of a simple time decaying factor of the form $t^{-{3}/{2}}$ and of an
essentially self-similar expansion. Apart from this self-similar expansion the
developed shell structure is preserved by the evolution. In particular, the
energy transported by each shell appears to be time independent.
