Geodesic
The porous media equation in an infinite cylinder, between two infinite parallel plates, and like spatial domains
Brian H. Gilding1 ; Jan Goncerzewicz2
1Kuwait University, Safat, Kuwait
2Wrocław University of Technology, Wroclaw, Poland
Interfaces and free boundaries, Tome 18 (2016) no. 1, pp. 45-73

Voir la notice de l'article provenant de la source EMS Press

DOI

The porous media equation has played a prominent role in the current development of the mathematical theory of interfaces and free boundaries. One occurs whenever the equation is solved in an unbounded spatial domain with initial data that have bounded support, and its appearance is of relevance to the physical and biological phenomena that the equation models. For a number of commonly studied spatial domains, the large-time behaviour of a solution of the porous media equation and of the solution’s free boundary is known. The present paper is concerned with this topic for a class of spatial domains which includes an infinite and a semi-infinite strip in two-dimensional space, an infinite and a semi-infinite cylinder of arbitrary cross-section in three-dimensional space, certain subdomains of these domains, and, their higher dimensional analogues. The homogeneous Cauchy–Dirichlet problem with initial data that are locally integrable is considered. Dependent upon the dimensionality, it is shown that there is a universal pattern of convergence to a self-similar solution. Moreover, the large-time behaviour of the free boundary in every solution mimics that of the self-similar one. The results rely on the establishment of an invariance principle for solutions of the problem.
DOI : 10.4171/ifb/356
Classification : 35-XX
Mots-clés : Porous media equation, large-time behaviour, free boundary, interface

Brian H. Gilding  1   ; Jan Goncerzewicz  2

1 Kuwait University, Safat, Kuwait
2 Wrocław University of Technology, Wroclaw, Poland 
Brian H. Gilding; Jan Goncerzewicz. The porous media equation in an infinite cylinder, between two infinite parallel plates, and like spatial domains. Interfaces and free boundaries, Tome 18 (2016) no. 1, pp. 45-73. doi: 10.4171/ifb/356
@article{10_4171_ifb_356,
     author = {Brian H. Gilding and Jan Goncerzewicz},
     title = {The porous media equation in an infinite cylinder, between two infinite parallel plates, and like spatial domains},
     journal = {Interfaces and free boundaries},
     pages = {45--73},
     year = {2016},
     volume = {18},
     number = {1},
     doi = {10.4171/ifb/356},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/356/}
}
TY  - JOUR
AU  - Brian H. Gilding
AU  - Jan Goncerzewicz
TI  - The porous media equation in an infinite cylinder, between two infinite parallel plates, and like spatial domains
JO  - Interfaces and free boundaries
PY  - 2016
SP  - 45
EP  - 73
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/356/
DO  - 10.4171/ifb/356
ID  - 10_4171_ifb_356
ER  - 
%0 Journal Article
%A Brian H. Gilding
%A Jan Goncerzewicz
%T The porous media equation in an infinite cylinder, between two infinite parallel plates, and like spatial domains
%J Interfaces and free boundaries
%D 2016
%P 45-73
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/356/
%R 10.4171/ifb/356
%F 10_4171_ifb_356

Cité par Sources :