Stability properties for nonlinear diffusion in porous and other media (Q1399313)

The paper is devoted to the investigation of nonlinear diffusion. A peculiarity of the problem is that the diffusivity is a function of the dependent variable. In particular, the porous medium model can be described in this way, the dependent variable being interpreted as a mass concentration. The equilibrium state is specified by a boundary value problem, and the unsteady state is determined by an initial boundary value problem with the initial value corresponding to an initial perturbation from the steady state. A Lyapunov functional as an integral, positive definite measure of perturbation is introduced and two upper estimates for this functional are obtained, implying global stability of the steady state.