  We study the evolution of supernova core from the beginning of gravitational
collapse of a 15Msolar star up to 1 second after core bounce. We present
results of spherically symmetric simulations of core-collapse supernovae by
solving general relativistic neutrino-radiation-hydrodynamics in the implicit
time-differencing. We aim to explore the evolution of shock wave in a long term
and investigate the formation of protoneutron star together with supernova
neutrino signatures. These studies are done to examine the influence of
equation of state (EOS) on the postbounce evolution of shock wave in the late
phase and the resulting thermal evolution of protoneutron star. We make a
comparison of two sets of EOS, that is, by Lattimer and Swesty (LS-EOS) and by
Shen et al.(SH-EOS). We found that, for both EOSs, the core does not explode
and the shock wave stalls similarly in the first 100 milliseconds after bounce.
The revival of shock wave does not occur even after a long period in either
cases. However, the recession of shock wave appears different beyond 200
milliseconds after bounce, having different thermal evolution of central core.
A more compact protoneutron star is found for LS-EOS than SH-EOS with a
difference in the central density by a factor of ~2 and a difference of ~10 MeV
in the peak temperature. Resulting spectra of supernova neutrinos are different
to the extent that may be detectable by terrestrial neutrino detectors.
