Source solutions for the nonlinear diffusion-convection equation

Abstract

In the paper King [8], a new class of source solutions was derived for the nonlinear diffusion equation for diffusivities of the form D(c) = D0cm /(1 -νc)m+2. Here we extend this method for the nonlinear diffusion and convection equation ∂c/∂t = ∂/∂z [D(c)∂c/∂z - K(c)], to obtain mass-conserving source solutions for a nonlinear conductivity function K(c) = K0cm+2/(1 - νc)m+1. In particular we consider the cases m = -1, 0, and 1, where fully analytical solutions are available. Furthermore we provide source solutions for the exponential forms of the diffusivity and conductivity as given by D(c) = D0c-2e-n/c and K(c) = K0ce-n/c. © Australian Mathematical Society, 1997.