Long time asymptotics of a system for plasma diffusion

We analyze a system of parabolic nonlinear equations that describe the diffusion of a fully collisional plasma across a strong magnetic field. We demonstrate that the solution to this system tends to a time asymptotic state which is of space-time separable form, ϕ(t)f(x). Furthermore, f(x) is independent of the initial conditions and ϕ(t) depends slightly on the initial conditions. The rate of decay of the temporal part is governed by a nonlinear eigenvalue problem. Since the equations are considered in a bounded domain we are able to analyze the effect of boundary conditions on the evolution of the system. Additional effects as radiation, heating, and particle injection can also be accounted for. Essential differences between the behavior of a fully-coupled system and a scalar equation are observed.