Positive semigroups and perturbations of boundary conditions

TL;DR

This paper establishes a generation theorem for positive semigroups on L^1 spaces, offering conditions for solutions to boundary value problems and applying it to a cell cycle model.

Contribution

It introduces a new generation theorem for positive semigroups and applies it to biological models, expanding the understanding of boundary condition perturbations.

Findings

Provides sufficient conditions for positive solutions

Applies theorem to a two-phase cell cycle model

Enhances methods for boundary condition perturbations

Abstract

We present a generation theorem for positive semigroups on an $L^1$ space. It provides sufficient conditions for the existence of positive and integrable solutions of initial-boundary value problems. An application to a two-phase cell cycle model is given.