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oai:docta.ucm.es:20.500.14352/647582023-08-11T07:46:18Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Elliot, C. M. author Herrero, Miguel A. author King, J. R. author Ockendon, J.R. author 1986 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. 0272-4960 10.1093/imamat/37.2.147 https://hdl.handle.net/20.500.14352/64758 http://imamat.oxfordjournals.org/content/37/2/147.short http://imamat.oxfordjournals.org The mesa problem: diffusion patterns for ut=∇⋅(um∇u) as m→+∞ .