Geodesic
On support of solutions to singular nonlinear parabolic equations in bounded domains
Fabio Punzo1
1Università degli Studi di Milano, Italy
Interfaces and free boundaries, Tome 13 (2011) no. 3, pp. 397-410

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

DOI

We investigate support properties of nonnegative solutions to nonlinear parabolic equations with variable density in bounded domains. The density can diverge or vanish near the boundary. Assuming that the initial datum has support not intersecting the boundary, we provide simple conditions, in dependence on the behaviour of the density, guaranteeing that the support of every nonnegative solution intersects the boundary at some positive time, or, in the case of convex domains, that it remains away from it for any positive time. These results extend to the case of bounded domains those given in [KK] for the Cauchy problem.
DOI : 10.4171/ifb/264
Classification : 35-XX, 00-XX
Mots-clés : Support of solutions; sub- and supersolutions; comparison principles

Fabio Punzo  1

1 Università degli Studi di Milano, Italy 
Fabio Punzo. On support of solutions to singular nonlinear parabolic equations in bounded domains. Interfaces and free boundaries, Tome 13 (2011) no. 3, pp. 397-410. doi: 10.4171/ifb/264
@article{10_4171_ifb_264,
     author = {Fabio Punzo},
     title = {On support of solutions to singular nonlinear parabolic equations in bounded domains},
     journal = {Interfaces and free boundaries},
     pages = {397--410},
     year = {2011},
     volume = {13},
     number = {3},
     doi = {10.4171/ifb/264},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/264/}
}
TY  - JOUR
AU  - Fabio Punzo
TI  - On support of solutions to singular nonlinear parabolic equations in bounded domains
JO  - Interfaces and free boundaries
PY  - 2011
SP  - 397
EP  - 410
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/264/
DO  - 10.4171/ifb/264
ID  - 10_4171_ifb_264
ER  - 
%0 Journal Article
%A Fabio Punzo
%T On support of solutions to singular nonlinear parabolic equations in bounded domains
%J Interfaces and free boundaries
%D 2011
%P 397-410
%V 13
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/264/
%R 10.4171/ifb/264
%F 10_4171_ifb_264

Cité par Sources :