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On the Kuramoto-Sivashinsky equation in a disk

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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.
Opis fizyczny
  • Departamento de Matemáticas, Escuela Colombiana de Ingenierí a, A.A. 14520, Bogotá, Colombia
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