  We study a class of one-dimensional, nonequilibrium, conserved growth
equations for both nonconserved and conserved noise statistics using numerical
integration. An atomistic version of these growth equations is also studied
using stochastic simulation. The models with nonconserved noise statistics are
found to exhibit mound formation and power-law coarsening with slope selection
for a range of values of the model parameters. Unlike previously proposed
models of mound formation, the Ehrlich-Schwoebel step-edge barrier, usually
modeled as a linear instability in growth equations, is absent in our models.
Mound formation in our models occurs due to a nonlinear instability in which
the height (depth) of spontaneously generated pillars (grooves) increases
rapidly if the initial height (depth) is sufficiently large. When this
instability is controlled by the introduction of an infinite number of
higher-order gradient nonlinearities, the system exhibits a first-order
dynamical phase transition from a rough self-affine phase to a mounded one as
the value of the parameter that measures the effectiveness of control is
decreased. We define a new ``order parameter'' that may be used to distinguish
between these two phases. In the mounded phase, the system exhibits power-law
coarsening of the mounds in which a selected slope is retained at all times.
The coarsening exponents for the continuum equation and the discrete model are
found to be different. An explanation of this difference is proposed and
verified by simulations. In the growth equation with conserved noise, we find
the curious result that the kinetically rough and mounded phases are both
locally stable in a region of parameter space. In this region, the initial
configuration of the system determines its steady-state behavior.
