Nonlinear effects in thermal wave propagation near zero absolute temperature

The nonlinear theory of thermal wave propagation at low temperatures, i.e. in the realm of hyperbolic heat conduction, is discussed with regard to implications of experimental data and numerical calculations. Simplifying assumptions of earlier approaches are replaced by a consequent nonlinear thermodynamics. The effects of nonlinearity on the solution behavior are investigated. In particular, Lax conditions on shock waves are analyzed and temperature ranges of admissibility for discontinuities are identified.