Delta shock solution to the generalized one-dimensional zero-pressure gas dynamics system with linear damping

TL;DR

This paper establishes the existence of delta shock solutions for a specific 2x2 conservation law system with linear damping using a vanishing viscosity approach, contributing to the mathematical understanding of such systems.

Contribution

It introduces a viscous approximation method to prove delta shock solutions for a generalized zero-pressure gas dynamics system with damping.

Findings

Existence of delta shock solutions demonstrated

Application of vanishing viscosity method to the system

Advancement in understanding damping effects in conservation laws

Abstract

In this paper, we propose a time-dependent viscous system and by using the vanishing viscosity method we show the existence of delta shock solution for a particular $2 \times 2$ system of conservation laws with linear damping.