一类非线性梁方程全局吸引子的维数估计

Dimension estimate for global attractor of a class of nonlinear beam equation

非线性梁方程描述了桥面竖直平面内的振动.在以往文献的基础上证明了一类非线性梁方程生成的解半群S(t)在全局吸引子Α上是一致可微,其全局吸引子具有有限的分形维数,并进一步应用Sobolev-LiebThirring不等式进行估计,得到全局吸引子的分形维数的上界.

The nonlinear beam equations represent the viberation of the rode bed in downward direction .Based on the existence of global attractors in other article ,this paper proved that semigroup S（t） generated by a class of nonlinear beam equation was uniformly differentiable on the global attractor Α.The paper also proved that global attractors of this class of equation have limited fractal dimension .Furthermore ,an estimate was given with the application of Sobolev-Lieb-Thirring inequality and upper bound of fractal dimension of the global attractor is obtained .