  W28 is one of the archetype supernova remnants (SNRs) interacting with
molecular clouds. H.E.S.S. observation found four TeV sources which are
coincident with the molecular clouds (MCs) around W28, but Fermi LAT detected
no prominent GeV counterparts for two of them. An accumulative diffusion model
is established in this Letter and the energetic protons colliding the nearby
MCs are considered to be an accumulation of the diffusive protons escaping from
the shock front throughout the history of the SNR expansion. We have fitted the
gamma ray spectra of the four sources and naturally explained the GeV spectral
break of the northeastern source (source N) and the nonsignificant GeV emission
of the southern sources A and C. The distances of sources A and C from the SNR
centre are found to be much larger than those of sources N and B, which may be
the basic reason for the faint GeV gamma rays of the two former sources.
