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On the dissipative Boussinesq equation in a non-cylindrical domain. (English) Zbl 1117.35307
Summary: We investigate the initial-boundary value problem for the one-dimensional nonlinear Boussinesq equation inside domains with moving ends having both small increasing and decreasing displacements. Global solvability, uniqueness of solutions and the exponential decay to the energy are established provided the initial data are bounded in some sense.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
32Q35 Complex manifolds as subdomains of Euclidean space
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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