Original Article
Published 2025-10-15
Keywords
- Boltzmann equation, force term, fixed point, non-continuous operator, Hardy–Rogers theorem.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
In this paper we study the local uniqueness of solutions to the Boltzmann equation with an external force term. Assuming the existence of solutions, we prove a local uniqueness result by applying a fixed point theorem of Hardy–Rogers. The collision operator is assumed to be bilinear, symmetric, and non-continuous, which allows extending previous results that require continuity assumptions. The obtained conditions contribute to the uniqueness theory for Boltzmann-type equations with force terms.