Applications of p-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions

Abstract

In a very general setting, we discuss possibilities of applying p-adics to geophysics using a p-adic diffusion representation of the master equations for the dynamics of a fluid in capillaries in porous media and formulate several mathematical problems motivated by such applications. We stress that p-adic wavelets are a powerful tool for obtaining analytic solutions of diffusion equations. Because p-adic diffusion is a special case of fractional diffusion, which is closely related to the fractal structure of the configuration space, p-adic geophysics can be regarded as a new approach to fractal modeling of geophysical processes.