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Asymptotic L1-decay of solutions of the porous medium equation to self-similarity
Carrillo de la Plata, José Antonio (University of Texas at Austin. Department of Mathematics)
Toscani., G. (University of Pavia. Department of Mathematics)

Date: 2000
Abstract: We consider the flow of gas in an N -dimensional porous medium with initial density v0 (x) ≥ 0. The density v(x, t) then satisfies the nonlinear degenerate parabolic equation vt = ∆v m where m > 1 is a physical constant. Assuming that (1 + $2 )v0 (x) dx < ∞, we prove that v(x, t) behaves asymptotically, as t → ∞, like the Barenblatt-Pattle solution V ( $, t). We prove that the L1 -distance decays at a rate t 1/((N+2)m−N) . Moreover, if N = 1, we obtain an explicit time decay for the L∞ distance at a suboptimal rate. The method we use is based on recent results we obtained for the Fokker-Planck equation [2], [3].
Rights: Tots els drets reservats.
Language: Anglès
Document: article ; publishedVersion
Published in: Indiana University mathematics journal, Vol. 49, No. 1 (2000) , p. 113-142, ISSN 0022-2518

DOI: 10.1512/iumj.2000.49.1756

30 p, 250.6 KB

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 Record created 2014-02-03, last modified 2021-02-27

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