%0 Journal Article
%A Elliot, C. M.
%A Herrero, Miguel A.
%A King, J. R.
%A Ockendon, J.R.
%T The mesa problem: diffusion patterns for ut=∇⋅(um∇u) as m→+∞ .
%D 1986
%@ 0272-4960
%U https://hdl.handle.net/20.500.14352/64758
%X 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.
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