Telegrapher's equations with variable propagation speeds

Abstract

All derivations of the one-dimensional telegrapher's equation, based on the persistent random walk model, assume a constant speed of signal propagation. We generalize here the model to allow for a variable propagation speed and study several limiting cases in detail. We also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes. © 1994 The American Physical Society.