Abstract
The two-dimensional damped Boussinesq equation with a forcing term is considered in a unit disc. It governs forced, small, nonlinear oscillations of a thin elastic membrane in the presence of viscosity. The eigenfunction expansion method is used for constructing global-in-time solutions of the initial-boundary-value problem in question. Specially designed anisotropic Sobolev spaces are introduced in order to reflect the effect of nonlinear smoothing in the angular coordinate. Existence and uniqueness in these spaces are proved on the basis of the construction. To cite this article: V. Varlamov, C. R. Mecanique 335 (2007).
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