On the dissipative Boussinesq equation in a non-cylindrical domain

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Abstract

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. © 2006 Elsevier Ltd. All rights reserved.

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Clark, H. R., Cousin, A. T., Frota, C. L., & Límaco, J. (2007). On the dissipative Boussinesq equation in a non-cylindrical domain. Nonlinear Analysis, Theory, Methods and Applications, 67(8), 2321–2334. https://doi.org/10.1016/j.na.2006.09.009

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