Well-posedness results for a sixth-order logarithmic Boussinesq equation

Abstract

The main goal of this paper is to study for a sixth-order logarithmic Boussinesq equation. We obtain several results: Firstly, by using Feado-Galerkin method and a logaritmic Sobolev inequality, we proved global existence of solutions. Later, we proved blow up property in infinity time of solutions. Finally, we showed the decay estimates result of the solutions. for two-way propagation of shallow water waves. For contributions related to (2), we refer to [4, 5, 10-14]. Wazwaz [15] studied the logarithmic Boussinesq equation (log-BE) the following form u tt − u xx + u xxxx + u log |u| k xx = 0.

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