  The presented paper is devoted to the search for mathematical basis for
describing the aftershock evolution of strong earthquakes. We consider the
experimental facts and heuristic arguments that allow to make a choice and to
focus on the nonlinear diffusion equation as the master equation. Analysis of
the master equation indicates that, apparently, the selected mathematical basis
makes it possible to simulate two important properties of the aftershock
evolution known from the experiment. We are talking about the Omori law and the
slow propagation of aftershocks from the epicenter of the main shock. Keywords:
earthquakes, propagation of aftershocks, Omori law, deactivation coefficient,
nonlinear diffusion, master equation, inverse problem
