  In this study, we treat the Fermi bubbles as a scaled-up version of supernova
remnants (SNRs). The bubbles are created through activities of the
super-massive black hole (SMBH) or starbursts at the Galactic center (GC).
Cosmic-rays (CRs) are accelerated at the forward shocks of the bubbles like
SNRs, which means that we cannot decide whether the bubbles were created by the
SMBH or starbursts from the radiation from the CRs. We follow the evolution of
CR distribution by solving a diffusion-advection equation, considering the
reduction of the diffusion coefficient by CR streaming. In this model,
gamma-rays are created through hadronic interaction between CR protons and the
gas in the Galactic halo. In the GeV band, we can well reproduce the observed
flat distribution of gamma-ray surface brightness, because some amount of gas
is left behind the shock. The edge of the bubbles is fairly sharp owing to the
high gas density behind the shock and the reduction of the diffusion
coefficient there. The latter also contributes the hard gamma-ray spectrum of
the bubbles. We find that the CR acceleration at the shock has started when the
bubbles were small, and the time-scale of the energy injection at the GC was
much smaller than the age of the bubbles. We predict that if CRs are
accelerated to the TeV regime, the apparent bubble size should be larger in the
TeV band, which could be used to discriminate our hadronic model from other
leptonic models. We also present neutrino fluxes.
