  In this paper, we prove that a particular nondegenerate, nonlinear,
autonomous parabolic partial differential equation with a nonlocal mass
transfer admits the local existence of classical solutions. The equation was
developed to qualitatively describe temporal changes in population densities
over space through accounting for location desirability and fast, long-range
travel. Beginning with sufficiently regular initial conditions, through
smoothing the PDE and employing energy arguments, we obtain a sequence of
approximators converging to a classical solution.
