Transport equations and perturbations of boundary conditions

TL;DR

This paper extends Kato's perturbation theorem to non-densely defined operators, applying it to transport equations and boundary conditions in Markov processes, with illustrative examples.

Contribution

It introduces a new perturbation theorem for substochastic semigroups on AL spaces, broadening the scope of existing perturbation results.

Findings

Extended perturbation theorem for non-densely defined operators

Application to transport equations with abstract boundary conditions

Illustrative examples demonstrating the theorem's utility

Abstract

We provide a new perturbation theorem for substochastic semigroups on abstract AL spaces extending Kato's perturbation theorem to non-densely defined operators. We show how it can be applied to piecewise deterministic Markov processes and transport equations with abstract boundary conditions. We give particular examples to illustrate our results.