  The space-time evolution of an inhomogeneous as well as homogeneous
condensate is studied. We use the $ \lambda \phi^4 $ model and adopt the
interaction representation in which the particle picture of the field $\phi$
with mass $m$ is definitely obtained. As the initial condition, a coherent
state is assumed. In the case of the homogeneous condensate, the amplitude of
it grows continuously with time and the perturbative calculation breaks down
for large time. On the other hand, in the case of the inhomogeneous condensate
with a finite initial size $\sim R$, the behavior of it is so different from
that of the homogeneous one. For $0< t < m R^2/2 $, the growth of the amplitude
of the inhomogeneous condensate at the origin $ ({\boldsymbol x}={\bf 0}) $ is
slowed down compared with that of the homogeneous one, and the contribution of
the interaction term $ (\lambda /4) :\phi^4: $ is restricted to the small
region around the origin of the condensate. For the late time, $ t > m R^2/2 $,
the condensate spreads into space.
