Асимптотики и невязка уравнения Фишера-Колмогорова-Петровского-Пискунова с аномальной диффузией

Abstract

Asymptotic solutions to the nonlocal one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation with fractional derivatives in the diffusion operator are constructed. Fractional derivative is determined in accordance with the Weil, Grunwald-Letnikov and Liouville approaches. Asymptotic solutions in a class of functions that are perturbations of a quasi-steady-state exact solution are found. The asymptotics constructed tend to this quasi-steady-state solution at large times. It is shown that the fractional derivatives lead to drift of the mass center of the system and break the symmetry of the initial distribution.