Existence and uniqueness of solutions for a boundary value problem arising from granular matter theory

TL;DR

This paper establishes the existence and uniqueness of solutions for a PDE system modeling granular matter, using a new weak formulation that aligns with the physical model.

Contribution

It introduces a novel weak formulation for a Monge-Kantorovich type PDE system, enabling rigorous proof of solution existence and uniqueness.

Findings

Proved existence of solutions under general conditions.

Established uniqueness of solutions for the PDE system.

Provided a physically consistent weak formulation.

Abstract

We consider a system of PDEs of Monge-Kantorovich type that, in the isotropic case, describes the stationary configurations of two-layers models in granular matter theory with a general source and a general boundary data. We propose a new weak formulation which is consistent with the physical model and permits us to prove existence and uniqueness results.