Probability density functions as solutions of heterogeneous Cattaneo-Vernotte diffusion equation

Abstract

In this paper, we considered a heterogeneous Cattaneo-Vernotte equation with an exponential type of diffusion coefficient under the fundamental initial and boundary conditions stating that the solution vanishes at $+/-$ infinity. Owing to the Laplace transform method we obtain two forms of exact analytical solutions which are presented in terms of the ratio of modified Bessel functions. Using the theory of complete monotone functions, we show that the obtained solutions are probability density functions.