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)
Fecha: |
2000 |
Resumen: |
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]. |
Derechos: |
Tots els drets reservats. |
Lengua: |
Anglès |
Documento: |
Article ; Versió publicada |
Publicado en: |
Indiana University mathematics journal, Vol. 49, No. 1 (2000) , p. 113-142, ISSN 0022-2518 |
DOI: 10.1512/iumj.2000.49.1756
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