  We study holographic thermalization of a strongly coupled theory inspired by
two colliding shock waves in a vacuum confining background. Holographic
thermalization means a black hole formation, in fact a trapped surface
formation. As a vacuum confining background we considered a well know bottom-up
AdS/QCD model that provides the Cornell potential as well as reproduces QCD
beta-function. We perturb vacuum background by colliding domain shock waves,
that are assumed to be holographically dual to heavy ions collisions. Our main
physical assumption is that we can make a restriction on the time of a trapped
surface production that makes a natural limitation on the size of the domain
where the trapped surface is produced. This limits the intermediate domain
where the main part of the entropy is produced. In this domain one can use an
intermediate vacuum background as an approximation to the full confining
background. In this intermediate background a dependence of the produced
entropy on colliding energy is very similar to the experimental dependence of
particles multiplicities on colliding ions energy obtained from RHIC and LHC.
This permits us to conclude that the entropy produced in collisions of domain
shock waves during a short time models rather well the experimental data.
