# Signed Radon measure-valued solutions of flux saturated scalar conservation laws

## TL;DR

This paper establishes existence and uniqueness of signed Radon measure-valued entropy solutions for scalar conservation laws with initial data as superpositions of Dirac masses, extending the understanding of measure-valued solutions.

## Contribution

It introduces a new class of measure-valued solutions for scalar conservation laws with signed Radon measures and proves their well-posedness under specific conditions.

## Key findings

- Existence of measure-valued entropy solutions
- Uniqueness under additional conditions
- Applicable to initial data as superpositions of Dirac masses

## Abstract

We prove existence and uniqueness for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension. The initial data of the problem is a finite superposition of Dirac masses, whereas the flux is Lipschitz continuous and bounded. The solution class is determined by an additional condition which is needed to prove uniqueness.