Kernel sections and global dynamics of nonautonomous Euler–Bernoulli beam equations

This paper concerns with dynamical behavior for nonautonomous Euler–Bernoulli beam equations with either weakly damping or strongly damping. Issues relevant to existence and Hausdorff dimension estimation of Kernel sections are investigated. It is shown that there exist Kernel sections for the beams, in the case of strongly damping, the techniques rely on splitting method, when the damping is weakly, the proof depends on the stabilization estimations of the system. Moreover, the Hausdorff dimension of Kernel sections is proved to be finite. Eventually, the global dynamics of the beams are studied by numerical simulation on the Kernel Sections and Kernel.