Some nonlinear problems of magnetodiffusion in the particle ensemble own field

1D and 2D equations of dynamics of magnetic particles concentration distribution due to the long-range forces of their own magnetic field are proposed. It has been found that magnetic interaction causes effective diffusion which intensity, in the case of sufficiently large particles, may be considerably higher than that of the thermal diffusion. The locally 1D method was used to develop numerical algorithm of the solution of nonlinear problems of magnetodiffusion. The plane front of magnetic particle concentration has been shown to be stable with respect to periodical perturbations, and this allows to conclude about hydrodynamic instabilities as the main cause of structure formation if the concentration is inhomogeneous.