Carleman estimate and unique continuation for a structured population model

TL;DR

This paper develops a Carleman estimate for a structured population model and uses it to prove unique continuation, showing that boundary data uniquely determine the solution.

Contribution

The paper introduces a new Carleman estimate for a structured population model and applies it to establish unique continuation properties.

Findings

Established a Carleman estimate for the model

Proved unique continuation from boundary data

Demonstrated boundary data determines the solution uniquely

Abstract

We consider a time-dependent structured population model equation and establish a Carleman estimate. We apply the Carleman estimate to prove the unique continuation which means that Cauchy data on any lateral boundary determine the solution uniquely.