Weak asymptotic solution of one dimensional zero pressure dynamics system in the quarter plane

TL;DR

This paper develops weak asymptotic solutions for a one-dimensional zero pressure system in the quarter plane, relevant to physical phenomena and queueing models, analyzing wave interactions with boundary Riemann solutions.

Contribution

It introduces a method to construct weak asymptotic solutions for boundary value problems involving wave interactions in the quarter plane.

Findings

Successfully constructs weak asymptotic solutions for the system.

Analyzes wave interactions with boundary Riemann solutions.

Provides a framework applicable to physical and queueing models.

Abstract

In this paper we study a system of equations which appear in the modelling of many physical phenomena. Initially this system appeared in description of the large scale structure formation. Recently it is derived as a second order queueing model. We construct weakly asymptotic solutions of the initial boundary value problem for the system and interaction of waves in the quarter plane $\{(x,t): x>0,t>0\}$ with boundary Riemann solution centered at $(0,0)$ and Riemann solution centered at a point $(x_0,0), x_0>0$.