Nonlinear hyperbolic heat conduction problem: Closed-form solutions

A nonlinear rigid heat conductor obeying the first and second laws of thermodynamics, Cattaneo's law, and a generalized energy-entropy relation in which both the energy and entropy are parabolic functions of the heat flux, is revisited. For a one-dimensional Cauchy problem in which both the temperature and heat flux are time-dependent only, a solution in terms of elementary functions is obtained. Also, for a one-dimensional traveling wave problem, a solution in terms of elementary functions is presented. Graphs illustrating the solutions are included.