The nonlinear wave and diffusion processes in media with a jump change in characteristics depending on the amplitude of the field distribution

Abstract

The models of nonlinear wave and diffusion processes with the stepwise change in equation coefficients in dependence of the solution amplitude and with non-fixed boundaries are proposed. The exact non-smooth solutions of the problems formulated are found. The positions of the boundary between the regions where the solutions are greater than the threshold value of the switching field and the regions where the solutions are less than the threshold value of the switching field are calculated. This position for the diffusion processes determines the phase transition boundary. It is proposed to use the calculated positions of the phase transition boundaries to estimate the diffusion coefficients by the experimentally determined parameters. The new formulations of the problems with non-fixed boundaries describing the nonlinear steady-state diffusion processes are considered in different geometry system. The various cases of diffusion regimes at the boundaries were studied analytically in each system.