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

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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

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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. http://geodesic.mathdoc.fr/articles/10.4064/ap-73-3-227-256/

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