  We simulate a growth model with restricted surface relaxation process in d=1
and d=2, where d is the dimensionality of a flat substrate. In this model, each
particle can relax on the surface to a local minimum, as the Edwards-Wilkinson
linear model, but only within a distance s. If the local minimum is out from
this distance, the particle evaporates through a refuse mechanism similar to
the Kim-Kosterlitz nonlinear model. In d=1, the growth exponent beta, measured
from the temporal behavior of roughness, indicates that in the coarse-grained
limit, the linear term of the Kardar-Parisi-Zhang equation dominates in short
times (low-roughness) and, in asymptotic times, the nonlinear term prevails.
The crossover between linear and nonlinear behaviors occurs in a characteristic
time t_c which only depends on the magnitude of the parameter s, related to the
nonlinear term. In d=2, we find indications of a similar crossover, that is,
logarithmic temporal behavior of roughness in short times and power law
behavior in asymptotic times.
