Delta shock wave formation in the case of triangular hyperbolic system of conservation laws

TL;DR

This paper investigates the formation of delta shock waves in a triangular hyperbolic system of conservation laws derived from a generalized pressureless gas dynamics model, using the weak asymptotic method.

Contribution

It introduces a novel analysis of delta shock wave formation in a specific hyperbolic system with continuous initial data, employing the weak asymptotic method.

Findings

Delta shock waves can form from continuous initial data in the system.

The weak asymptotic method effectively describes the shock wave formation.

Results extend understanding of pressureless gas dynamics models.

Abstract

We describe $\delta$ shock wave arising from continuous initial data in the case of triangular conservation law system arising from "generalized pressureless gas dynamics model". We use the weak asymptotic method.