Geodesic
Finite speed of propagation for the thin-film equation and other higher-order parabolic equations with general nonlinearity
Daniele Andreucci1 ; Anatoli Tedeev2
1Università di Roma La Sapienza, Italy
2Vladikavkaz Scientific Center of the RAS, Russian Federation
Interfaces and free boundaries, Tome 3 (2001) no. 3, pp. 233-264

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

DOI

We prove the property of finite speed of propagation for degenerate parabolic equations of order 2m [ges] 2, when the nonlinearity is of general type, and not necessarily a power function. We also give estimates of the growth in time of the interface bounding the support of the solution. In the case of the thin-film equation, with non-power nonlinearity, we obtain sharp results, in the range of nonlinearities we consider. Our optimality result seems to be new even in the case of power nonlinearities with general initial data. In the case of the Cauchy problem for degenerate equations with general m, our main assumption is a suitable integrability Dini condition to be satisfied by the nonlinearity itself. Our results generalize Bernis' estimates for higher-order equations with power structures. In the case of second-order equations we also prove L[infin] estimates of solutions.
DOI : 10.4171/ifb/40
Classification : 46-XX, 60-XX
Mots-clés : finite speed propagation, thin films, degenerate parabolic equations

Daniele Andreucci  1   ; Anatoli Tedeev  2

1 Università di Roma La Sapienza, Italy
2 Vladikavkaz Scientific Center of the RAS, Russian Federation 
Daniele Andreucci; Anatoli Tedeev. Finite speed of propagation for the thin-film equation and other higher-order parabolic equations with general nonlinearity. Interfaces and free boundaries, Tome 3 (2001) no. 3, pp. 233-264. doi: 10.4171/ifb/40
@article{10_4171_ifb_40,
     author = {Daniele Andreucci and Anatoli Tedeev},
     title = {Finite speed of propagation for the thin-film equation and other higher-order parabolic equations with general nonlinearity},
     journal = {Interfaces and free boundaries},
     pages = {233--264},
     year = {2001},
     volume = {3},
     number = {3},
     doi = {10.4171/ifb/40},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/40/}
}
TY  - JOUR
AU  - Daniele Andreucci
AU  - Anatoli Tedeev
TI  - Finite speed of propagation for the thin-film equation and other higher-order parabolic equations with general nonlinearity
JO  - Interfaces and free boundaries
PY  - 2001
SP  - 233
EP  - 264
VL  - 3
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/40/
DO  - 10.4171/ifb/40
ID  - 10_4171_ifb_40
ER  - 
%0 Journal Article
%A Daniele Andreucci
%A Anatoli Tedeev
%T Finite speed of propagation for the thin-film equation and other higher-order parabolic equations with general nonlinearity
%J Interfaces and free boundaries
%D 2001
%P 233-264
%V 3
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/40/
%R 10.4171/ifb/40
%F 10_4171_ifb_40

Cité par Sources :