Perturbations of superstable linear hyperbolic systems

The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems 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 C1 under small bounded perturbations. To show this for C1, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually C1-smooth for any L2-initial data.