| Abstract: |
| The Cauchy problem for the nonlinear one-dimensional sixth-order Boussinesq equation with logarithmic nonlinearity is concerned in this paper. This model describes the propagation of long waves on the surface of water within small amplitude. The main motivation of this paper is to reveal how logarithmic nonlinearity $u \ln |u|^k$ along with the higher-order dispersive term $u_{ x x x x x x }$ affects the qualitative properties of the solution. Some of the efforts on results of global existence and exponential growth of the solution are shown. The main tools to obtain these results include the logarithmic Sobolev inequality, Galerkin method and the concave method. The initial energy is divided into different cases by the depth of the potential well, and corresponding results for subcritical and critical energy levels are both given. |
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