Observability inequalities for degenerate transport equations

TL;DR

This paper establishes an observability inequality for a degenerate transport equation by deriving a local Carleman estimate and extending it to a global result through energy estimates.

Contribution

It introduces a novel local Carleman estimate for degenerate transport equations and uses it to prove a global observability inequality.

Findings

Established a local Carleman estimate for degenerate transport equations

Derived a global observability inequality from the local estimate

Provided a new analytical tool for control theory of degenerate PDEs

Abstract

In this paper we prove an observability inequality for a degenerate transport equation. First we introduce a local in time Carleman estimate for the degenerate equation, then we apply it to obtain a global in time observability inequality by using also an energy estimate.