Affiliation:
1. Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy New York USA
2. Department of Physics Clark Atlanta University Atlanta Georgia USA
Abstract
AbstractThe simple heat conduction equation in one‐space dimension does not have the property of a finite speed for information transfer. A partial resolution of this difficulty can be obtained within the context of heat conduction by the introduction of a partial differential equation (PDE) called the Maxwell–Cattaneo (M‐C) equation, elsewhere called the damped wave equation, a special case of the telegraph equation. We construct a generalization to the M‐C equation by allowing the relaxation time parameter to be a function of temperature. In the balance of the paper, we present a variety of special exact and approximate solutions to this nonlinear PDE.