We prove the existence of kernel sections for the
process generated by a damped non-autonomous wave equation when there
is nonlinear damping and the nonlinearity has a critically growing exponent.
We show uniform boundedness of the Hausdorff dimension of the
kernel sections. Finally, we point out that in the case of autonomous
systems with linear damping, the obtained upper bound of the Hausdorff
dimension decreases as the damping grows for suitable large damping.