A perturbation theorem for positive contraction semigroups on L 1-spaces with applications to transport equations and Kolmogorov's differential equations

In this paper, a criterion is given for assuring that a linear positive contraction C ₀-semigroup defined on an L ¹-space is generated by the closure of A+B, A and B being suitable unbounded linear operators. Furthermore, this criterion is applied to the transport equation, Kolmogorov's differential equations, and a transport equation modelling cell growth.