A new generation criterion theorem for C0-semigroups implying a generalization of Kaiser-Weis-Batty's perturbation theorem

By proving existence, regularity and uniqueness of solutions to Cauchy problems governed by abstract unbounded operators with finite pseudo-spectral bounds as an alternative and a serious enhancement of results by Melnikova and Filinkov, we establish a new generation criterion theorem for C-0-semigroups in general Banach spaces. A generalization of Kaiser-Weis-Batty's perturbation generation theorem in reflexive Banach spaces is therefore derived. We apply our last theoretical result to a singular transport model in L-p-spaces, p is an element of]1, +infinity[, where the streaming (unperturbed) semigroup cannot be explicit.