Istituto di Matematica Applicata e Tecnologie Informatiche     
Carrillo J. A., Toscani G. Asymptotic L^1 decay of solutions of the porous medium equation to self-similarity. Technical report ercim.cnr.ian//1998-1099, 1998.
We consider the flow of gas in an N-dimensional porous medium with nonnegative initial density. The density v(x,t) then satisfies a nonlinear degenerate diffusion parabolic equation. Assuming that the initial density has finite mass and energy, we prove that v(x,t) behaves asymptotically, as t tends to infinity, like the Barenblatt-Pattle similarity solution. In particular we find that the L1 distance decays at a polinomial rate. Moreover, if N=1, we obtain an explicit time decay for the distance in L at a suboptimal rate. The method we use is based on recent results we obtained for the linear Fokker-Planck equation.
Subject Porous media

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