具阻尼项的Boussinesq型方程的长时间行为

Long Time Behavior of Boussinesq Type Equation with Damping Term

该文研究具阻尼项的Boussinesq型方程utt-△u＋△^2u-△ut-△g（u）=f（x）初边值问题的解的长时间行为.利用半群分解的方法证明了上述问题对应的无穷维动力系统在能量相空间E=V2×H中整体吸引子的存在性和吸引子Hausdorff维数的有限性,其中对非线性项g（u）的抽象条件加以验证并给出具体实例.

In this paper, we study the long time behavior of the solution of the initial boundary value problem of Boussinesq type equation with damping term： utt-△u＋△^2u-△ut-△g（u）=f（x）. The main result is that the existence of global attractor of the infinite dimensional dynamical system and the existence of the global attractor and the Hausdorff dimension of the attractor in the phase space E=V2×H are proved by the method of semi group decomposition, The abstract condition of nonlinear term g（u） is verified and given a concrete example.