The object of this paper is to study a sixth-order Boussinesq equation with dispersive, linear strong damping and nonlinear source by using potential well methods, including the following aspects: firstly, the local well-posedness of the solutions is studied; secondly, the global existence and the finite time blow-up conditions are studied at two different initial energy levels by using the relationship between the initial energy and the depth of the potential well; thirdly, a blow-up condition independent of the depth of the potential well is established and by using of this condition, the existence of blow-up solutions at arbitrary initial energy level is studied; finally, the upper bound estimation of blow-up time and some necessary and sufficient conditions for existing finite time blow-up solutions are established.

本文的目的是利用势阱法研究具有色散、线性强阻尼和非线性源的六阶Boussinesq方程，包括以下几个方面：首先，研究解的局部适定性；其次，利用初始能量与势阱深度的关系，研究了两个不同初始能级下的全局存在和有限时间爆破条件；第三，建立了与势阱深度无关的爆破条件，并利用该条件研究了任意初始能级爆破解的存在性；最后，建立了爆破时间的上限估计和现有有限时间爆破解的一些充要条件。