Geodesic
Global solvability of the Kuramoto-Sivashinsky equation with bounded initial data
Sbornik. Mathematics, Tome 200 (2009) no. 7, pp. 1075-1088

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The paper considers initial-boundary-value problems for the Kuramoto-Sivashinsky equation both with Dirichlet boundary conditions and with Navier-type boundary conditions when $t>0$ and $x\in\Omega\subset\mathbb R^N$, $N\le3$. Given bounded initial data, the problems in question are shown to be uniquely globally (in $t>0$) solvable in relevant classes of functions. Bibliography: 21 titles.
Keywords: non-linear equations, a priori estimate, global solvability, the Kuramoto-Sivashinsky equation. 
@article{SM_2009_200_7_a3,
     author = {S. I. Pokhozhaev},
     title = {Global solvability of the {Kuramoto-Sivashinsky} equation with bounded initial data},
     journal = {Sbornik. Mathematics},
     pages = {1075--1088},
     publisher = {mathdoc},
     volume = {200},
     number = {7},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_7_a3/}
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S. I. Pokhozhaev. Global solvability of the Kuramoto-Sivashinsky equation with bounded initial data. Sbornik. Mathematics, Tome 200 (2009) no. 7, pp. 1075-1088. http://geodesic.mathdoc.fr/item/SM_2009_200_7_a3/