Diffusion equation in mathematical geomorphology

Abstract

Solutions of diffusion equations which describe pattern of the relief evolution have been analysed and an ambiguity is shown to be present in the basic definitions of the enthropy and time direction in geomorphic processes. To exclude the ambiguity it is suggested to deduce the enthropy of geomorphic systems from their hypsographic functions (i. e. functions of height distribution). When concerning the real evolution of the relief with many states of equilibrium and non-equilibrium, possibilities of the process description using diffusion equations are shown to be limited. The necessity is emphasized to use more complex mathematical technique of the dymanic systems theory.