On the stability of first order PDEs associated to vector fields

Abstract

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

Keywords: Hyers-Ulam stability; partial differential equation; vector field; flow