A nonhomogeneous boundary value problem in mass transfer theory

TL;DR

This paper establishes the uniqueness of solutions for a class of PDEs related to mass transfer, under mild regularity conditions, and characterizes stationary solutions in granular matter theory when using Euclidean metrics.

Contribution

It provides a new uniqueness theorem for Monge-Kantorovich type PDEs with minimal regularity assumptions and describes stationary solutions in a specific physical context.

Findings

Proved uniqueness of solutions under mild regularity assumptions.

Characterized stationary solutions in granular matter theory with Euclidean metrics.

Extended the understanding of mass transfer PDEs in nonhomogeneous settings.

Abstract

We prove a uniqueness result of solutions for a system of PDEs of Monge-Kantorovich type arising in problems of mass transfer theory. The results are obtained under very mild regularity assumptions both on the reference set $\Omega\subset\mathbf{R}^n$, and on the (possibly asymmetric) norm defined in $\Omega$. In the special case when $\Omega$ is endowed with the Euclidean metric, our results provide a complete description of the stationary solutions to the tray table problem in granular matter theory.