  In this talk we present our detail study ( theory and numbers) [1] on the
shadowing corrections to the gluon structure functions for nuclei. Starting
from rather contraversial information on the nucleon structure function which
is originated by the recent HERA data, we develop the Glauber approach for the
gluon density in a nucleus based on Mueller formula [2] and estimate the value
of the shadowing corrections in this case. Than we calculate the first
corrections to the Glauber approach and show that these corrections are big.
Based on this practical observation we suggest the new evolution equation which
takes into account the shadowing corrections and solve it. We hope to convince
you that the new evolution equation gives a good theoretical tool to treat the
shadowing corrections for the gluons density in a nucleus and, therefore, it is
able to provide the theoretically reliable initial conditions for the time
evolution of the nucleus - nucleus cascade.
