Semigroups of max-plus linear operators

TL;DR

This paper introduces and analyzes strongly continuous max-plus linear operator semigroups, providing foundational properties and examples from non-linear evolution equations, advancing the understanding of max-plus algebra applications.

Contribution

It defines and studies the properties of max-plus linear semigroups, including key examples from non-linear evolution equations, which is a novel contribution to the field.

Findings

Established properties of max-plus linear semigroups

Presented examples from non-linear evolution equations

Extended the theory of operator semigroups in max-plus algebra

Abstract

We define strongly continuous max-additive and max-plus linear operator semigroups and study their main properties. We present some important examples of such semigroups coming from non-linear evolution equations.