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

A new result for the porous medium equation derived from the Ricci flow