On the stability of first order PDEs associated to vector fields

TL;DR

This paper investigates the Hyers-Ulam stability of first-order PDEs linked to vector fields on manifolds, focusing on solutions' stability properties in Banach spaces.

Contribution

It provides a new analysis of stability conditions for differential equations involving vector fields on manifolds, extending previous results to a broader geometric setting.

Findings

Established criteria for Hyers-Ulam stability of the PDEs

Extended stability analysis to manifold settings

Identified conditions on vector fields and functions for stability

Abstract

Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\rightarrow B$ and any fixed complex number $\lambda$, we study Hyers-Ulam stability of the global differential equation $Vy=\lambda y+f$.