The mesa problem: diffusion patterns for ut=∇⋅(um∇u) as m→+∞ .



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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

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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
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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