2026-06-29T07:26:50Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/647582023-08-11T07:46:18Zcom_20.500.14352_14col_20.500.14352_15
The mesa problem: diffusion patterns for ut=∇⋅(um∇u) as m→+∞ .
Elliot, C. M.
Herrero, Miguel A.
King, J. R.
Ockendon, J.R.
517.9
517.956.4
Porous-medium equation
initial data
spatially independent
initial value
free boundary
Stefan problem
variational inequalities
singular-perturbation
structure of the transition region
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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.
Depto. de Análisis Matemático y Matemática Aplicada
Fac. de Ciencias Matemáticas
Instituto de Matemática Interdisciplinar (IMI)
TRUE
pub
2023-06-21T02:03:58Z
2023-06-21T02:03:58Z
1986
journal article
https://hdl.handle.net/20.500.14352/64758
0272-4960
10.1093/imamat/37.2.147
metadata only access
Oxford University Press