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 $L^2$ as well as in $C^1$ under small bounded perturbations. To show this for $C^1$, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually $C^1$-smooth for any $L^2$-initial data. 
I. Kmit and N. Lyul'ko
math.AP