一维完全非线性波动方程的一个注记

A Note on One-Dimension Fully Nonlinear Wave Equations

本文研究满足零条件的一维完全非线性波动方程的 Cauchy 问题,通过将一维完全非线性波动方程化为一维拟线性波动方程组,利用拟线性情形的结论,我们证明了小初值经典解的整体存在性。

In this paper, we study the Cauchy problem of one-dimension fully nonlinear wave equations with null condition, by transforming the one-dimension fully nonlinear wave equation to a system of one-dimension quasilinear wave equations, and using the result in the quasilinear case, we show the global existence of classical solution with small initial data.