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Elliot, C. M. and Herrero, Miguel A. and King, J. R. and Ockendon, J.R.
(1986)
*The mesa problem: diffusion patterns for ut=∇⋅(um∇u) as m→+∞ .*
IMA Journal of Applied Mathematics , 37
(2).
pp. 147-154.
ISSN 0272-4960

Official URL: http://imamat.oxfordjournals.org/content/37/2/147.short

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http://imamat.oxfordjournals.org | Organisation |

## Abstract

In this paper we consider the limit m→+∞ of solutions of the porous-medium equation ut = ∇•(um∇u)(xεRN), with N > 1. We conjecture that, for initial data with a unique maximum, the evolution is characterized by the onset of a ‘mesa’ region, in which the solution is nearly spatially independent, surrounded by a region in which u is nearly equal to its initial value. The transition between these regions occurs near a surface which is identified with the free boundary in a certain Stefan problem which can be studied using variational inequalities. Moreover, singular-perturbation theory can be used to describe the structure of the transition region.

Item Type: | Article |
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Uncontrolled Keywords: | Porous-medium equation; initial data; spatially independent; initial value; free boundary; Stefan problem; variational inequalities; singular-perturbation; structure of the transition region |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 18164 |

Deposited On: | 04 Feb 2013 09:31 |

Last Modified: | 12 Dec 2018 15:08 |

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