Linear Problems and Waves

Solutions of transport equations in simple settings are invaluable for the deeper understanding of the various transport phenomena. In this chapter we linearize the transport equations for small deviations from an equilibrium ground state, and study one-dimensional transport behavior. We focus on wave solutions, and study dispersion and damping for wave and diffusion equations. The Cattaneo equation is derived and discussed as an example of non-local transport, where the system is not in local equilibrium states.