Elliot, C. M.Herrero, Miguel A.King, J. R.Ockendon, J.R.2023-06-212023-06-2119860272-496010.1093/imamat/37.2.147https://hdl.handle.net/20.500.14352/64758In 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.journal articlehttp://imamat.oxfordjournals.org/content/37/2/147.shorthttp://imamat.oxfordjournals.orgmetadata only access517.9517.956.4Porous-medium equationinitial dataspatially independentinitial valuefree boundaryStefan problemvariational inequalitiessingular-perturbationstructure of the transition regionEcuaciones diferenciales1202.07 Ecuaciones en Diferencias