RT Journal Article
T1 The mesa problem: diffusion patterns for ut=∇⋅(um∇u) as m→+∞ .
A1 Elliot, C. M.
A1 Herrero, Miguel A.
A1 King, J. R.
A1 Ockendon, J.R.
AB 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.
PB Oxford University Press
SN 0272-4960
YR 1986
FD 1986
LK https://hdl.handle.net/20.500.14352/64758
UL https://hdl.handle.net/20.500.14352/64758
DS Docta Complutense
RD 12 abr 2025