On shape preserving semigroups

TL;DR

This paper introduces and analyzes shape preserving operator semigroups, focusing on their fundamental properties, stability under perturbations and limits, with applications to partial delay differential equations.

Contribution

It defines shape preserving semigroups and proves their stability properties, extending the theory to include perturbations, limits, and applications to delay differential equations.

Findings

Shape preserving semigroups are stable under perturbations.

They are preserved under taking limits.

Applications to partial delay differential equations are demonstrated.

Abstract

Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental properties. In particular, we prove that the class of shape preserving semigroups is preserved by perturbations and taking limits. These results are applied to partial delay differential equations.