  Given $\Bbb R^2, $ with a ``good'' complete metric, we show that the unique
solution of the Ricci flow approaches a soliton at time infinity. Solitons are
solutions of the Ricci flow, which move only by diffeomorphism. The Ricci flow
on $\Bbb R^2$ is the limiting case of the porous medium equation when $m$ is
zero. The results in the Ricci flow may therefore be interpreted as sufficient
conditions on the initial data, which guarantee that the corresponding unique
solution for the porous medium equation on the entire plane asymptotically
behaves like a ``soliton-solution''.
