# On the Kuramoto-Sivashinsky equation in a disk

Annales Polonici Mathematici (2000)

- Volume: 73, Issue: 3, page 227-256
- ISSN: 0066-2216

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topVarlamov, Vladimir. "On the Kuramoto-Sivashinsky equation in a disk." Annales Polonici Mathematici 73.3 (2000): 227-256. <http://eudml.org/doc/262852>.

@article{Varlamov2000,

abstract = {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.},

author = {Varlamov, Vladimir},

journal = {Annales Polonici Mathematici},

keywords = {first initial-boundary value problem; long-time asymptotics; Kuramoto-Sivashinsky equation; disk; uniform in space long-time asymptotic expansion; existence and the uniqueness of a global in time solution; small initial data},

language = {eng},

number = {3},

pages = {227-256},

title = {On the Kuramoto-Sivashinsky equation in a disk},

url = {http://eudml.org/doc/262852},

volume = {73},

year = {2000},

}

TY - JOUR

AU - Varlamov, Vladimir

TI - On the Kuramoto-Sivashinsky equation in a disk

JO - Annales Polonici Mathematici

PY - 2000

VL - 73

IS - 3

SP - 227

EP - 256

AB - 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.

LA - eng

KW - first initial-boundary value problem; long-time asymptotics; Kuramoto-Sivashinsky equation; disk; uniform in space long-time asymptotic expansion; existence and the uniqueness of a global in time solution; small initial data

UR - http://eudml.org/doc/262852

ER -

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