Local existence of solutions to a nonlinear autonomous PDE model for population dynamics with nonlocal transport and competition.

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with 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. • Partial differential equation models are ubiquitous in applied sciences. • A partial differential equation based in ecology is studied for solution existence. • Energy methods and convergence analysis lead to local classical solutions. [ABSTRACT FROM AUTHOR]