ON AN EXTENSION OF THE KATO-VOIGT PERTURBATION THEOREM FOR SUBSTOCHASTIC SEMIGROUPS AND ITS APPLICATION

Abstract

The aim of this paper is to discuss some recent developments of the perturbation method introduced first by Kato for the Kolmogoroff equation and later extended by Voigt and Arlotti to deal with a range of problems related to the solvability of the so-called Master Equation. The paper consists of two parts. In the first we recall and unify some abstract results on generation of substochastic semigroups. In the second we perform a detailed analysis of an equation from the polymer degradation theory to demonstrate a number of possible generation cases.