Local Existence of a Classical Solution for Quasi-Linear Hyperbolic Systems

TL;DR

This paper presents a new proof for the local existence of classical solutions to quasi-linear hyperbolic systems, focusing on convergence of derivatives via the Arzela-Ascoli theorem.

Contribution

It introduces a novel proof technique for local existence, emphasizing the convergence of derivatives in quasi-linear hyperbolic systems.

Findings

Established local existence of classical solutions

Demonstrated convergence of derivatives using Arzela-Ascoli theorem

Provided a new proof approach for hyperbolic systems

Abstract

In this paper, we study quasi-linear hyperbolic systems. Our goal in this paper is to provide a new proof of local existence of a classical solution for the system. Most difficult point is to prove the convergence of the derivative of approximate solutions by the Arzela-Ascoli theorem.