Asymptotic behavior of solutions to perturbed superstable wave equations

Abstract

The paper deals with initial-boundary value problems for the linear wave equation whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in L2 as well as in C2 under small bounded perturbations of the wave operator. To show this for C2, we prove a smoothing result implying that the solutions to the perturbed problems become eventually C2-smooth for any H1 × L2-initial data.