A LWR model with constraints at moving interfaces

TL;DR

This paper introduces a mathematical framework for scalar conservation laws with moving interfaces, focusing on a LWR model with flux constraints, and proves existence using a finite volume scheme with mesh modifications.

Contribution

It develops a novel framework for conservation laws with moving interfaces, including mesh modifications and trajectory crossing treatment, and proves existence of solutions.

Findings

Finite volume scheme successfully demonstrates existence.

Mesh modifications effectively handle moving interfaces.

Framework accommodates flux constraints at interfaces.

Abstract

We propose a mathematical framework to the study of scalar conservation laws with moving interfaces. This framework is developed on a LWR model with constraint on the flux along these moving interfaces. Existence is proved by means of a finite volume scheme. The originality lies in the local modification of the mesh and in the treatment of the crossing points of the trajectories.