On the uniqueness of solutions to continuity equations

TL;DR

This paper establishes sufficient conditions ensuring the uniqueness of solutions to the continuity equation for measure classes that are not necessarily absolutely continuous, expanding the understanding of solution behavior in measure spaces.

Contribution

It provides new criteria for uniqueness of solutions to the continuity equation in broader measure classes beyond absolutely continuous measures.

Findings

Identifies conditions guaranteeing uniqueness in measure solutions.

Extends classical results to non-absolutely continuous measures.

Enhances theoretical understanding of measure-valued solutions.

Abstract

We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.