Dynamic First Order Wave Systems with Drift Term on Riemannian Manifolds

TL;DR

This paper investigates a class of first-order hyperbolic differential equations with drift on Riemannian manifolds, establishing well-posedness through functional analytic methods involving transmutator and commutator relations.

Contribution

It introduces a new framework for analyzing hyperbolic equations with drift on manifolds, focusing on well-posedness using advanced functional analysis techniques.

Findings

Established well-posedness of the equations

Developed general transmutator and commutator relations

Extended analysis to Riemannian manifold setting

Abstract

An abstract first order differential equation of hyperbolic type with drift term on a Riemannian manifold is considered. For proving its well-posedness, transmutator and commutator relations are needed, which are studied in a general functional analytic setting.