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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Abstract

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

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

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357140405

Mathematical Reviews number (MathSciNet)
MR1852629

Zentralblatt MATH identifier
1007.35041

Subjects
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

Citation

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. https://projecteuclid.org/euclid.ade/1357140405.


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