1D pressureless gas dynamics systems in a strip

TL;DR

This paper develops explicit measure-valued solutions for 1D pressureless gas dynamics in a strip, highlighting boundary effects and singularity formation using a new boundary potential approach.

Contribution

It introduces a novel boundary potential method to construct measure-valued solutions and analyze boundary-induced mass accumulation in pressureless gas dynamics.

Findings

Solutions satisfy an entropy condition

Mass accumulation can occur at boundaries

Provides detailed understanding of singularity formation

Abstract

We construct explicit measure-valued solutions to the one-dimensional pressureless gas dynamics system in a strip-like domain by introducing a new boundary potential. The constructed solutions satisfy an entropy condition, and depending on the boundary data and the behavior of the potentials, mass accumulation can occur at the boundaries. The approach relies on a systematic treatment of boundary potentials and their interactions with the initial data, providing a more precise understanding of the formation and propagation of singularities in measure-valued solutions.