Kernel sections for non-autonomous strongly damped wave equations of non-degenerate Kirchhoff-type

摘要

We prove the existence of compact kernel sections for the process generated by strongly damped wave equations of non-degenerate Kirchhoff-type modelling the non-linear vibrations of an elastic string. And we obtain a precise estimate of upper bound of Hausdorff dimension of kernel sections, which decreases as the strong damping grows for large strong damping under some conditions, particularly in the autonomous case.