Remarks on the Asymptotic Behavior of Solutions to Damped Wave Equations in Hilbert Space.

摘要

Lower bounds are derived for the norms of solutions to a class of initial-value problems associated with the damped wave equation sub tt + Au sub t + Bu=0 in Hilbert space. Under appropriate assumptions on the linear operator B it is shown that even in the special strongly damped case where A = Gamma I, Gamma > 0, solutions are bounded way from zero as t approaches plus infinity, even when Gamma approaches plus infinity. (Author)