TY - JOUR

T1 - The asymptotic behavior of gas in an n-dimensional porous medium

AU - Friedman, Avner

AU - Kamin, Shoshana

PY - 1980/12

Y1 - 1980/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84968502599&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1980-0586735-0

DO - 10.1090/S0002-9947-1980-0586735-0

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AN - SCOPUS:84968502599

VL - 262

SP - 551

EP - 563

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -