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 -