  We study the transient start-up dynamics of a fluidity model which captures
the rheological behavior of aging soft glassy materials, in a rectilinear shear
flow upon application of step shear rate. We observe that when the steady state
flow curve is non-monotonic the system shows transient and/or apparent steady
state shear banding in close qualitative agreement with experimental
observations. Due to a competetion between aging and rejuvenation during the
start up, we show that there is an apparent steady state banding at large times
even for shear rates such that the steady state flow curve allows for a
homogeneous flow. Thus, for aging soft glassy materials, the shear rate for
achieving homogeneous flow is not necessarily given by the steady-state flow
curve. We also observe that the transient and apparent steady state shear
banding behavior is not correlated to negative slope of the stress-strain
dependence during the transient. This work also emphasizes that in order to
have a realistic description of shear banding behavior in the aging (time
dependent) soft glassy materials, consideration of inertia during the start-up
dynamics is crucial.
