  The spectral and spatiotemporal dynamics of photoluminescence in monolayers
of transition metal dichalcogenide WSe$_2$ obtained by mechanical exfoliation
on a Si/SiO$_2$ substrate is studied over a wide range of temperatures and
excitation powers. It is shown that the dynamics is nonexponential and, for
times $t$ exceeding $\sim$50 ps after the excitation pulse, is described by a
dependence of the form $1/(t+t_0)$. Photoluminescence decay is accelerated with
a decrease in temperature, as well as with a decrease in the energy of emitting
states. It is shown that the observed dynamics cannot be described by a
bimolecular recombination process, such as exciton--exciton annihilation. A
model that describes the nonexponential photoluminescence dynamics by taking
into account the spread of radiative recombination times of localized exciton
states in a random potential gives good agreement with experimental data.
