On a perturbed kernel in viscoelasticity

For a viscoelastic problem we consider a kernel satisfying the standard condition (the derivative of the kernel is smaller than or equal to a negative constant times the kernel itself) yielding exponential decay of the solutions. We perturb this relaxation function in such a manner that the standard condition is no longer satisfied (for any constant). It is proved that we still have exponential decay in the case where the L 1 -norm of the perturbation is small enough.