Semigroups for dynamical processes on metric graphs

TL;DR

This paper explores the use of operator semigroups to analyze dynamical systems on metric graphs, emphasizing well-posedness under standard vertex conditions and illustrating applications in biological models.

Contribution

It introduces an operator semigroup framework for first- and second-order systems on metric graphs, highlighting well-posedness and providing biological applications.

Findings

Established well-posedness for systems with standard vertex conditions

Surveyed existing results on semigroup approaches on metric graphs

Presented two biological model applications

Abstract

We present the operator semigroups approach to first- and second-order dynamical systems taking place on metric graphs. We briefly survey the existing results and focus on the well-posedness of the problems with standard vertex conditions. Finally, we show two applications to biological models.