Initial-boundary value problems for nearly incompressible vector fields, and applications to the Keyfitz and Kranzer system

TL;DR

This paper proves existence and uniqueness for initial boundary value problems involving nearly incompressible vector fields and applies these results to ensure well-posedness of the Keyfitz and Kranzer system in multiple dimensions.

Contribution

It introduces new mathematical results for nearly incompressible vector fields and applies them to a complex system of conservation laws, extending previous work.

Findings

Established existence and uniqueness for boundary value problems with nearly incompressible vector fields.

Proved well-posedness of the Keyfitz and Kranzer system in multiple space dimensions.

Abstract

We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and Kranzer system of conservation laws in several space dimensions.