Transport processes and traveling waves in systems with local nonequilibrium

Transport equations are studied for two types of media exhibiting properties of local nonequilibrium: media with thermal memory and media with a discrete structure. A hyperbolic transport equation that is a special case of these local-nonequilibrium equations is used for the analysis of traveling waves having high velocities. These waves have certain important properties: there can be a temperature discontinuity at the wave front; there exist thermal shock waves; the temperature at the wave front exceeds the equilibrium adiabatic value; there exist stationary autowave regimes in addition to those corresponding to the classical local-equilibrium case, and the velocities of these regimes are bounded by the velocity of propagation of a thermal signal. The approach developed here may be useful for the study of transport processes for short times or high fluxes in systems near critical points, in heterogeneous systems, and in other extremal situations.