  Solutions of hydrodynamical equations are presented for an equation of state
allowing for a first-order phase transition. The numerical analysis is
supplemented by analytical treatment provided the system is close to the
critical point. The processes of growth and dissolution of seeds of various
sizes and shapes in meta-stable phases (like super-cooled vapor and
super-heated liquid) are studied, as well as the dynamics of unstable modes in
the spinodal region. We show that initially nonspherical seeds acquire
spherical shape with passage of time. Applications to the description of the
first-order phase transitions in nuclear systems, such as the nuclear
gas-liquid transition occurring in low energy heavy-ion collisions and the
hadron-quark transition in the high energy heavy-ion collisions are discussed.
In both cases we point out the important role played by effects of viscosity
and surface tension. It is shown that fluctuations dissolve and grow as if the
fluid were effectively very viscous. Even in the spinodal region seeds may grow
slowly due to viscosity and critical slowing down. This prevents the
enhancement of fluctuations in the near-critical region, which is frequently
considered as a signal of the critical point in heavy-ion collisions.
