In this paper, the p‐Laplacian hyperbolic type equation with logarithmic nonlinearity and weak damping term are considered, where the global existence of solutions by using the potential well method is discussed. Furthermore, the growth and the decay estimates of solutions for the problem are studied.

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.

No abstract

No abstract

No abstract