  The very high energy gamma-ray source HESS J1809-193 has been detected by the
LHAASO and HAWC observatory beyond 100 TeV energy. It is an interesting
candidate for exploring the underlying mechanisms of gamma-ray production due
to the presence of supernova remnants, pulsar and molecular clouds close to it.
We have considered the injection of the energetic cosmic rays from a past
explosion, whose reminiscent may be SNR G011.0-00.0, which is located within
the extended gamma-ray source HESS J1809-193. We explain the multi-wavelength
data from the region of HESS J1809-193 with synchrotron, inverse Compton,
bremsstrahlung emission of cosmic ray electrons and secondary gamma-ray
production in interactions of cosmic ray protons with the cold protons in the
local molecular clouds within a time-dependent framework including the
diffusion loss of cosmic rays. The observational data has been modelled with
the secondary photons produced by the time-evolved cosmic ray spectrum,
assuming the age of the explosion is 4500 years.
