Well-posedness of non-autonomous transport equation on metric graphs

TL;DR

This paper proves the well-posedness of non-autonomous transport equations on metric graphs with time-dependent velocities, using evolution families and semigroups under continuity assumptions.

Contribution

It establishes the well-posedness of non-autonomous transport equations on metric graphs with time-dependent velocities, a novel extension in the mathematical analysis of such systems.

Findings

Well-posedness of the non-autonomous transport equation is proven.

Continuity of velocity coefficients ensures the mathematical well-posedness.

Uses evolution families and semigroups to analyze the problem.

Abstract

We consider transport processes on metric graphs with time-dependent velocities and show that, under continuity assumption of the velocity coefficients, the corresponding non-autonomous abstract Cauchy problem is well-posed by means of evolution families and evolution semigroups.