On the Diffusion of Immiscible Fluids in Porous Media

From the mathematical formulation of the diffusion of two immiscible fluids, we arrive at a nonlinear two-sided degenerate parabolic equation. Existence, uniqueness and a weak maximum principle are proved for the Cauchy problem in the half plane $x \in \mathbb{R}$, $t > 0$. Furthermore, it is sho...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 1979-05, Vol.10 (3), p.486-497
Main Author: van Duyn, C. J.
Format: Article
Language:English
Subjects:
Applied mathematics
Cauchy problems
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Summary:From the mathematical formulation of the diffusion of two immiscible fluids, we arrive at a nonlinear two-sided degenerate parabolic equation. Existence, uniqueness and a weak maximum principle are proved for the Cauchy problem in the half plane $x \in \mathbb{R}$, $t > 0$. Furthermore, it is shown that the solutions of a class of Cauchy problems converge towards a similarity solution as $t \to \infty $ and the rate of convergence is discussed.
ISSN:0036-1410
1095-7154
DOI:10.1137/0510046