The asymptotic behavior of gas in an n-dimensional porous medium

Avner Friedman, Shoshana Kamin

Research output: Contribution to journalArticlepeer-review

Abstract

Consider the flow of gas in an n-dimensional porous medium with initial density u0(x)> 0.The density u(x, t) then satisfies the nonlinear degenerate parabolic equation (Formula Presented) 1 is a physical constant. Assuming that (Formula Presented) it is proved that u(x, t) behaves asymptotically, as (Formula Presented), like the special (explicitly given) solution V(|x|, t) which is invariant by similarity transformations and which takes the initial values (Formula Presented) = the Dirac measure) in the distribution sense.

Original languageEnglish
Pages (from-to)551-563
Number of pages13
JournalTransactions of the American Mathematical Society
Volume262
Issue number2
DOIs
StatePublished - Dec 1980

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