Analysis of nonlinear parabolic equations modeling plasma diffusion across a magnetic field

The evolutionary behavior of the solution of a pair of coupled quasilinear parabolic equations modeling the diffusion of heat and mass of a magnetically confined plasma is analyzed. The solution's due to the nonlinear diffusion coefficients, exhibits many new phenomena. In short time, the solution converges into a highly organized symmetric pattern that is almost completely independent of initial data. The asymptotic dynamics then become very simple and take place in a finite demensional space. These conclusions are backed by extensive numerical experimentation.