Nonlinear Diffusion Problem Arising in Plasma Physics

In earlier studies of plasma diffusion with Okuda-Dawson scaling ($D\sim n^{-\frac{1}{2}}$), perturbation theory indicated that arbitrary initial data should evolve rapidly toward the separable solution of the relevant nonlinear diffusion equation. Now a Lyapunov functional has been found which is strictly decreasing in time and bounded below. The rigorous proof that arbitrary initial data evolve toward the separable solution is summarized. Rigorous bounds on the decay time are also presented.