Geodesic
On the Kuramoto-Sivashinsky equation in a disk
Annales Polonici Mathematici, Tome 73 (2000) no. 3, pp. 227-256

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider the first initial-boundary value problem for the 2-D Kuramoto-Sivashinsky equation in a unit disk with homogeneous boundary conditions, periodicity conditions in the angle, and small initial data. Apart from proving the existence and uniqueness of a global in time solution, we construct it in the form of a series in a small parameter present in the initial conditions. In the stable case we also obtain the uniform in space long-time asymptotic expansion of the constructed solution and its asymptotics with respect to the nonlinearity constant. The method can work for other dissipative parabolic equations with dispersion.
DOI : 10.4064/ap-73-3-227-256
Keywords: first initial-boundary value problem, long-time asymptotics, Kuramoto-Sivashinsky equation, disk

Vladimir Varlamov 1

1 
@article{10_4064_ap_73_3_227_256,
     author = {Vladimir Varlamov},
     title = {On the {Kuramoto-Sivashinsky} equation in a disk},
     journal = {Annales Polonici Mathematici},
     pages = {227--256},
     publisher = {mathdoc},
     volume = {73},
     number = {3},
     year = {2000},
     doi = {10.4064/ap-73-3-227-256},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-73-3-227-256/}
}
TY  - JOUR
AU  - Vladimir Varlamov
TI  - On the Kuramoto-Sivashinsky equation in a disk
JO  - Annales Polonici Mathematici
PY  - 2000
SP  - 227
EP  - 256
VL  - 73
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-73-3-227-256/
DO  - 10.4064/ap-73-3-227-256
LA  - en
ID  - 10_4064_ap_73_3_227_256
ER  - 
%0 Journal Article
%A Vladimir Varlamov
%T On the Kuramoto-Sivashinsky equation in a disk
%J Annales Polonici Mathematici
%D 2000
%P 227-256
%V 73
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-73-3-227-256/
%R 10.4064/ap-73-3-227-256
%G en
%F 10_4064_ap_73_3_227_256
Vladimir Varlamov. On the Kuramoto-Sivashinsky equation in a disk. Annales Polonici Mathematici, Tome 73 (2000) no. 3, pp. 227-256. doi: 10.4064/ap-73-3-227-256

Cité par Sources :