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Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium


Author: Juan Luis Vázquez
Journal: Trans. Amer. Math. Soc. 277 (1983), 507-527
MSC: Primary 35B40; Secondary 35K55, 76S05
DOI: https://doi.org/10.1090/S0002-9947-1983-0694373-7
MathSciNet review: 694373
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Abstract: The one-dimensional porous media equation $ {u_t} = {({u^m})_{xx}}$, $ m > 1$, is considered for $ x \in R$, $ t > 0$ with initial conditions $ u(x,0) = {u_0}(x)$ integrable, nonnegative and with compact support. We study the behaviour of the solutions as $ t \to \infty $ proving that the expressions for the density, pressure, local velocity and interfaces converge to those of a model solution. In particular the first term in the asymptotic development of the free-boundary is obtained.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0694373-7
Keywords: Flows in porous media, asymptotic behaviour, free boundaries, shiftingcomparison
Article copyright: © Copyright 1983 American Mathematical Society

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