Positively Invariant Subset for Non-Densely Defined Cauchy Problems

TL;DR

This paper establishes conditions under which a closed subset remains invariant under the evolution of semi-linear non-densely defined Cauchy problems, with applications to age-structured population models.

Contribution

It introduces a sub-tangential condition ensuring positive invariance for non-densely defined Cauchy problems, extending previous results to new classes of models.

Findings

Proves positive invariance under specified conditions

Applies results to age-structured population models

Provides a framework for analyzing non-dense Cauchy problems

Abstract

In this article we prove the positive invariance of a closed subset by the semiflow generated by a semi-linear non densely Cauchy problem. The condition impose to obtain such a property is a so called sub-tangential condition. We apply our results to a class of age structured population models.