Advances in Differential Equations

Intermediate asymptotics of the porous medium equation with sign changes

Mark Bowen, Josephus Hulshof, and John R. King

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We study the porous medium equation with sign changes and examine the way sign changes disappear. We give a formal classification of self-similar and non-self-similar scenarios for their disappearance, for $N>1,$ restricting attention to the radial case. The results we present on the classification of similarity solutions are rigorous except where indicated otherwise.

Article information

Adv. Differential Equations, Volume 6, Number 9 (2001), 1115-1152.

First available in Project Euclid: 2 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K70: Ultraparabolic equations, pseudoparabolic equations, etc.
Secondary: 35B40: Asymptotic behavior of solutions 35K57: Reaction-diffusion equations 35K65: Degenerate parabolic equations 76S05: Flows in porous media; filtration; seepage


Hulshof, Josephus; King, John R.; Bowen, Mark. Intermediate asymptotics of the porous medium equation with sign changes. Adv. Differential Equations 6 (2001), no. 9, 1115--1152.

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