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We present results of numerical simulations of galaxy formation with effects of radiative and compton cooling and feedback from supernovae explosions being taken into account. We found that the supernovae feedback has a very strong impact on the evolution of the gas components and the star-formation rate. For large galaxies this feedback results in a low, steady rate of the star-formation on the level of $(1-3)M_{\odot}$ per year for $z < 5$. Large galaxies (mass larger than $(2-3)\cdot 10^{11}M_{\odot}$ inside 100~kpc radius) have 2--3 times larger fraction of mass in baryons (stars + gas) as compared to the mean ratio in the Universe. The feedback has much stronger effect on the evolution of dwarf galaxies. Most of dwarf galaxies in our models have small amount stars and extremely low luminosities: $M_R>-15$ for mass of parent dark halo $M_{\rm tot}<(2-3)\cdot 10^{10}M_{\odot}$ inside 50~kpc radius. Dwarf galaxies, which are close to giants ($<0.5$~Mpc), are significantly brighter than those in low density areas.
We found that galaxies in the CDM models are systematically too red and, thus are too old as compared with real galaxies. We used the Bruzual \& Charlot (1992) stellar population synthesis models to track evolution of galaxy colors.
In our 3D numerical hydro+N-body simulations the matter is treated as a multi phase medium having four components: dark matter, hot baryonic gas and cold gas clouds (an analog of molecular clouds) embedded in the hot gas, and stars produced from the cold gas. Two phases of the gas roughly mimic the ISM and star formation in our Galaxy. Stars are allowed to form only inside clouds. Stars with mass $>10 M_{\odot}$ explode as supernova, which evaporate cold clouds around and heat the hot gas. We study models with initial fluctuations corresponding to the biased CDM model on scales from 50 kpc to 5 Mpc.
