  We investigate the inside structure of one-dimensional reaction-diffusion
traveling fronts. The reaction terms are of the monostable, bistable or
ignition types. Assuming that the fronts are made of several components with
identical diffusion and growth rates, we analyze the spreading properties of
each component. In the monostable case, the fronts are classified as pulled or
pushed ones, depending on the propagation speed. We prove that any localized
component of a pulled front converges locally to 0 at large times in the moving
frame of the front, while any component of a pushed front converges to a well
determined positive proportion of the front in the moving frame. These results
give a new and more complete interpretation of the pulled/pushed terminology
which extends the previous definitions to the case of general transition waves.
In particular, in the bistable and ignition cases, the fronts are proved to be
pushed as they share the same inside structure as the pushed monostable
critical fronts. Uniform convergence results and precise estimates of the left
and right spreading speeds of the components of pulled and pushed fronts are
also established.
