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
DOI: 10.12677/PM.2023.133069, PDF, HTML, 下载: 138  浏览: 211  科研立项经费支持
作者: 薛欣欣, 查冬兵：东华大学理学院数学系，上海
关键词: 一维完全非线性波动方程；Cauchy 问题；零条件；小初值；整体存在性；One-Dimension Fully Nonlinear Wave Equations； Cauchy Problem； Null Condition； Small Initial Data； Global Existence
摘要: 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。
Abstract: 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.
文章引用：薛欣欣, 查冬兵. 一维完全非线性波动方程的一个注记[J]. 理论数学, 2023, 13(3): 644-648. https://doi.org/10.12677/PM.2023.133069

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