Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium
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- by Juan Luis Vázquez PDF
- Trans. Amer. Math. Soc. 277 (1983), 507-527 Request permission
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.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- 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