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

Shih-Wei Chou, Ying-Chieh Lin, Naoki Tsuge

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.

Local Existence of a Classical Solution for Quasi-Linear 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.
Paper Structure (2 theorems, 58 equations)

This paper contains 2 theorems, 58 equations.

Key Result

Theorem 1

Suppose that $A$, $h$, and $\bar{u}$ satisfy the assumption (A). Then There exist constants $\Lambda,T>0$ and a continuously differentiable function $u$ which is the unique classical solution of quasilinear, ID on the domain

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • Lemma 2